Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was ad...Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.展开更多
The bedform-driven hyporheic exchange plays a crucial role in mass transport within natural aquatic ecosystems like streams and rivers. This study aimed to unveil the impact of geometric features of impermeable discre...The bedform-driven hyporheic exchange plays a crucial role in mass transport within natural aquatic ecosystems like streams and rivers. This study aimed to unveil the impact of geometric features of impermeable discrete bedforms on hyporheic exchange by experimentally measuring quantitative hyporheic exchange flux data and variation characteristics in an annual flume. The experiments encompassed diverse conditions involving the ratio of bedform wavelength (λ) to wave height (h) and relative submergence. The study also analyzed the dependence of the effective diffusion coefficient on the geometric characteristics of bedform composition elements. The experimental results showed that, in comparison to a permeable flat bed, the presence of an impermeable discrete bedform tended to either attenuate or enhance hyporheic exchange, contingent on the geometric characteristics of bedform composition elements. The hyporheic exchange flux exhibited an initially increase followed by a decrease with increasing λ/h, with turbulence penetration emerging as the dominant mechanism governing hyporheic exchange for cases with relatively denser bedform composition elements (e.g., λ/h = 4.0). The effective diffusion coefficient peaked at λ/h around 6.0–8.0, owing to a significant augmentation in the relative contribution of pumping exchange to gross hyporheic exchange. Furthermore, the hyporheic exchange intensity generally increased with decreasing relative submergence, primarily attributed to the augmented relative contribution of pumping exchange to gross hyporheic exchange.展开更多
It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponent...It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.展开更多
The aim of this study is to compare the Discrete wavelet decomposition and the modified Principal Analysis Component (PCA) decomposition to analyze the stabilogram for the purpose to provide a new insight about human ...The aim of this study is to compare the Discrete wavelet decomposition and the modified Principal Analysis Component (PCA) decomposition to analyze the stabilogram for the purpose to provide a new insight about human postural stability. Discrete wavelet analysis is used to decompose the stabilogram into several timescale components (i.e. detail wavelet coefficients and approximation wavelet coefficients). Whereas, the modified PCA decomposition is applied to decompose the stabilogram into three components, namely: trend, rambling and trembling. Based on the modified PCA analysis, the trace of analytic trembling and rambling in the complex plan highlights a unique rotation center. The same property is found when considering the detail wavelet coefficients. Based on this property, the area of the circle in which 95% of the trace’s data points are located, is extracted to provide important information about the postural equilibrium status of healthy subjects (average age 31 ± 11 years). Based on experimental results, this parameter seems to be a valuable parameter in order to highlight the effect of visual entries, stabilogram direction, gender and age on the postural stability. Obtained results show also that wavelets and the modified PCA decomposition can discriminate the subjects by gender which is particularly interesting in biometric applications and human stability simulation. Moreover, both techniques highlight the fact that male are less stable than female and the fact that there is no correlation between human stability and his age (under 60).展开更多
In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving...In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.展开更多
Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal...Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal and heuristic procedures. This allows one to obtain quasi-optimal solutions after a small number of steps, overcoming the NP-completeness of discrete optimization problems. Questions of constructing so-called “duplicate” algorithms are considered to improve the quality of discrete problem solutions. An approach to solving discrete problems with fuzzy coefficients in objective functions and constraints on the basis of modifying the generalized algorithms is considered. Questions of applying the generalized algorithms to solve multicriteria discrete problems are also discussed. The results of the paper are of a universal character and can be applied to the design, planning, operation, and control of systems and processes of different purposes. The results of the paper are already being used to solve power engineering problems.展开更多
The coefficient of rolling friction is a foundation parameter for conducting particles simulation,however,which of irregularly shaped maize seeds is difficult to measure.Furthermore,the coefficient of rolling friction...The coefficient of rolling friction is a foundation parameter for conducting particles simulation,however,which of irregularly shaped maize seeds is difficult to measure.Furthermore,the coefficient of rolling friction between the simulation particles and the actual seeds is inconsistent due to the shaped difference of model and different position of gravity center.This paper use two methods to determinate the coefficient of rolling friction based on discrete element method(DEM)and physical experiments.Three types of maize models from five different shaped maize samples(including horse-tooth shape,spherical cone shape,spherical shape,oblate shape,irregular shape)were developed with the help of slice modeling and 3D modeling technology.Aluminum cylinder container is used to arrange the simulation experiments of angle of repose with taking the coefficient of rolling friction as independent variables and the simulation angle of repose as target values.After predicting detailed the coefficient of rolling friction(including horse-tooth shape,spherical cone shape,spherical shape,between horse-tooth shape and spherical cone shape,between horse-tooth shape and spherical shape,between spherical shape and spherical cone shape maize models),and forecasting a unified the coefficient of rolling friction among horse-tooth shape,spherical cone shape and spherical shape maize models,two types of materials(aluminum cylinder container and organic glass container)were used to validate the difference the angle of repose between the simulation maize models and actual maize seeds.Results show the relative error of the angle of repose between the maize models controlled by the coefficient of rolling friction through the detailed method and the actual maize seeds is 0.22%,0.33%in aluminum cylinder,organic glass container,respectively.The relative error of the angle of repose between the simulation maize models controlled by the coefficient of rolling friction through the united method and actual maize seeds is 2.47%,2.97%in aluminum cylinder,organic glass container,respectively.Although the difference of the angle of repose between two method is smaller,the detailed method is better.Moreover,From the accumulation process of the angle of repose we found that the difference on the contacts number between maize models and bottom plate,the change curve of the rotational kinetic energy,the potential energy of maize models controlled by the coefficient of rolling friction through the detailed and the united method are evidently.We can choose a better method to predict the coefficient of rolling friction of maize seeds according to the application situation and investigation objective of irregular maize seeds.The results can provide a theoretical basis for designing and optimizing the structure of the seed-metering machine with DEM.展开更多
It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasona...It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.展开更多
A method combining the pseudo-dynamic approach and discretization technique is carried out for computing the active earth pressure.Instead of using a presupposed failure mechanism,discretization technique is introduce...A method combining the pseudo-dynamic approach and discretization technique is carried out for computing the active earth pressure.Instead of using a presupposed failure mechanism,discretization technique is introduced to generate the potential failure surface,which is applicable to the case that soil strength parameters have spatial variability.For the purpose of analyzing the effect of earthquake,pseudo-dynamic approach is adopted to introduce the seismic forces,which can take into account the dynamic properties of seismic acceleration.A new type of micro-element is used to calculate the rate of work of external forces and the rate of internal energy dissipation.The analytical expression of seismic active earth pressure coefficient is deduced in the light of upper bound theorem and the corresponding upper bound solutions are obtained through numerical optimization.The method is validated by comparing the results of this paper with those reported in literatures.The parametric analysis is finally presented to further expound the effect of diverse parameters on active earth pressure under non-uniform soil.展开更多
Essential proteins play a vital role in biological processes,and the combination of gene expression profiles with Protein-Protein Interaction(PPI)networks can improve the identification of essential proteins.However,g...Essential proteins play a vital role in biological processes,and the combination of gene expression profiles with Protein-Protein Interaction(PPI)networks can improve the identification of essential proteins.However,gene expression data are prone to significant fluctuations due to noise interference in topological networks.In this work,we discretized gene expression data and used the discrete similarities of the gene expression spectrum to eliminate noise fluctuation.We then proposed the Pearson Jaccard coefficient(PJC)that consisted of continuous and discrete similarities in the gene expression data.Using the graph theory as the basis,we fused the newly proposed similarity coefficient with the existing network topology prediction algorithm at each protein node to recognize essential proteins.This strategy exhibited a high recognition rate and good specificity.We validated the new similarity coefficient PJC on PPI datasets of Krogan,Gavin,and DIP of yeast species and evaluated the results by receiver operating characteristic analysis,jackknife analysis,top analysis,and accuracy analysis.Compared with that of node-based network topology centrality and fusion biological information centrality methods,the new similarity coefficient PJC showed a significantly improved prediction performance for essential proteins in DC,IC,Eigenvector centrality,subgraph centrality,betweenness centrality,closeness centrality,NC,PeC,and WDC.We also compared the PJC coefficient with other methods using the NF-PIN algorithm,which predicts proteins by constructing active PPI networks through dynamic gene expression.The experimental results proved that our newly proposed similarity coefficient PJC has superior advantages in predicting essential proteins.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 1...We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.展开更多
基金This work was supported by the National Natural Science Foundation of China,NSFC(Nos.U1803118 and 51974296)and the China Scholarship Council(CSC)(award to Fanfei Meng for PhD period at Kyushu University).
文摘Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.
基金supported by the National Natural Science Foundation of China(Grant No.11472168).
文摘The bedform-driven hyporheic exchange plays a crucial role in mass transport within natural aquatic ecosystems like streams and rivers. This study aimed to unveil the impact of geometric features of impermeable discrete bedforms on hyporheic exchange by experimentally measuring quantitative hyporheic exchange flux data and variation characteristics in an annual flume. The experiments encompassed diverse conditions involving the ratio of bedform wavelength (λ) to wave height (h) and relative submergence. The study also analyzed the dependence of the effective diffusion coefficient on the geometric characteristics of bedform composition elements. The experimental results showed that, in comparison to a permeable flat bed, the presence of an impermeable discrete bedform tended to either attenuate or enhance hyporheic exchange, contingent on the geometric characteristics of bedform composition elements. The hyporheic exchange flux exhibited an initially increase followed by a decrease with increasing λ/h, with turbulence penetration emerging as the dominant mechanism governing hyporheic exchange for cases with relatively denser bedform composition elements (e.g., λ/h = 4.0). The effective diffusion coefficient peaked at λ/h around 6.0–8.0, owing to a significant augmentation in the relative contribution of pumping exchange to gross hyporheic exchange. Furthermore, the hyporheic exchange intensity generally increased with decreasing relative submergence, primarily attributed to the augmented relative contribution of pumping exchange to gross hyporheic exchange.
基金Supported by the National Natural Science Foundations of China( 1 9631 0 4 0 ) and SSFC( o2 BTJ0 0 1 ) .
文摘It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.
文摘The aim of this study is to compare the Discrete wavelet decomposition and the modified Principal Analysis Component (PCA) decomposition to analyze the stabilogram for the purpose to provide a new insight about human postural stability. Discrete wavelet analysis is used to decompose the stabilogram into several timescale components (i.e. detail wavelet coefficients and approximation wavelet coefficients). Whereas, the modified PCA decomposition is applied to decompose the stabilogram into three components, namely: trend, rambling and trembling. Based on the modified PCA analysis, the trace of analytic trembling and rambling in the complex plan highlights a unique rotation center. The same property is found when considering the detail wavelet coefficients. Based on this property, the area of the circle in which 95% of the trace’s data points are located, is extracted to provide important information about the postural equilibrium status of healthy subjects (average age 31 ± 11 years). Based on experimental results, this parameter seems to be a valuable parameter in order to highlight the effect of visual entries, stabilogram direction, gender and age on the postural stability. Obtained results show also that wavelets and the modified PCA decomposition can discriminate the subjects by gender which is particularly interesting in biometric applications and human stability simulation. Moreover, both techniques highlight the fact that male are less stable than female and the fact that there is no correlation between human stability and his age (under 60).
基金the Council of Scientific and Industrial Research,New Delhi,India for its financial support.
文摘In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.
文摘Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal and heuristic procedures. This allows one to obtain quasi-optimal solutions after a small number of steps, overcoming the NP-completeness of discrete optimization problems. Questions of constructing so-called “duplicate” algorithms are considered to improve the quality of discrete problem solutions. An approach to solving discrete problems with fuzzy coefficients in objective functions and constraints on the basis of modifying the generalized algorithms is considered. Questions of applying the generalized algorithms to solve multicriteria discrete problems are also discussed. The results of the paper are of a universal character and can be applied to the design, planning, operation, and control of systems and processes of different purposes. The results of the paper are already being used to solve power engineering problems.
基金This work was supported financially by the Chinese Natural Science Foundation(51405086,51665001)Discipline construction fund project of Gansu Agricultural University(GAU-XKJS-2018-193).
文摘The coefficient of rolling friction is a foundation parameter for conducting particles simulation,however,which of irregularly shaped maize seeds is difficult to measure.Furthermore,the coefficient of rolling friction between the simulation particles and the actual seeds is inconsistent due to the shaped difference of model and different position of gravity center.This paper use two methods to determinate the coefficient of rolling friction based on discrete element method(DEM)and physical experiments.Three types of maize models from five different shaped maize samples(including horse-tooth shape,spherical cone shape,spherical shape,oblate shape,irregular shape)were developed with the help of slice modeling and 3D modeling technology.Aluminum cylinder container is used to arrange the simulation experiments of angle of repose with taking the coefficient of rolling friction as independent variables and the simulation angle of repose as target values.After predicting detailed the coefficient of rolling friction(including horse-tooth shape,spherical cone shape,spherical shape,between horse-tooth shape and spherical cone shape,between horse-tooth shape and spherical shape,between spherical shape and spherical cone shape maize models),and forecasting a unified the coefficient of rolling friction among horse-tooth shape,spherical cone shape and spherical shape maize models,two types of materials(aluminum cylinder container and organic glass container)were used to validate the difference the angle of repose between the simulation maize models and actual maize seeds.Results show the relative error of the angle of repose between the maize models controlled by the coefficient of rolling friction through the detailed method and the actual maize seeds is 0.22%,0.33%in aluminum cylinder,organic glass container,respectively.The relative error of the angle of repose between the simulation maize models controlled by the coefficient of rolling friction through the united method and actual maize seeds is 2.47%,2.97%in aluminum cylinder,organic glass container,respectively.Although the difference of the angle of repose between two method is smaller,the detailed method is better.Moreover,From the accumulation process of the angle of repose we found that the difference on the contacts number between maize models and bottom plate,the change curve of the rotational kinetic energy,the potential energy of maize models controlled by the coefficient of rolling friction through the detailed and the united method are evidently.We can choose a better method to predict the coefficient of rolling friction of maize seeds according to the application situation and investigation objective of irregular maize seeds.The results can provide a theoretical basis for designing and optimizing the structure of the seed-metering machine with DEM.
文摘It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.
基金Projects(51908557,51378510)supported by the National Natural Science Foundation of China。
文摘A method combining the pseudo-dynamic approach and discretization technique is carried out for computing the active earth pressure.Instead of using a presupposed failure mechanism,discretization technique is introduced to generate the potential failure surface,which is applicable to the case that soil strength parameters have spatial variability.For the purpose of analyzing the effect of earthquake,pseudo-dynamic approach is adopted to introduce the seismic forces,which can take into account the dynamic properties of seismic acceleration.A new type of micro-element is used to calculate the rate of work of external forces and the rate of internal energy dissipation.The analytical expression of seismic active earth pressure coefficient is deduced in the light of upper bound theorem and the corresponding upper bound solutions are obtained through numerical optimization.The method is validated by comparing the results of this paper with those reported in literatures.The parametric analysis is finally presented to further expound the effect of diverse parameters on active earth pressure under non-uniform soil.
基金supported by the Shenzhen KQTD Project(No.KQTD20200820113106007)China Scholarship Council(No.201906725017)+2 种基金the Collaborative Education Project of Industry-University cooperation of the Chinese Ministry of Education(No.201902098015)the Teaching Reform Project of Hunan Normal University(No.82)the National Undergraduate Training Program for Innovation(No.202110542004).
文摘Essential proteins play a vital role in biological processes,and the combination of gene expression profiles with Protein-Protein Interaction(PPI)networks can improve the identification of essential proteins.However,gene expression data are prone to significant fluctuations due to noise interference in topological networks.In this work,we discretized gene expression data and used the discrete similarities of the gene expression spectrum to eliminate noise fluctuation.We then proposed the Pearson Jaccard coefficient(PJC)that consisted of continuous and discrete similarities in the gene expression data.Using the graph theory as the basis,we fused the newly proposed similarity coefficient with the existing network topology prediction algorithm at each protein node to recognize essential proteins.This strategy exhibited a high recognition rate and good specificity.We validated the new similarity coefficient PJC on PPI datasets of Krogan,Gavin,and DIP of yeast species and evaluated the results by receiver operating characteristic analysis,jackknife analysis,top analysis,and accuracy analysis.Compared with that of node-based network topology centrality and fusion biological information centrality methods,the new similarity coefficient PJC showed a significantly improved prediction performance for essential proteins in DC,IC,Eigenvector centrality,subgraph centrality,betweenness centrality,closeness centrality,NC,PeC,and WDC.We also compared the PJC coefficient with other methods using the NF-PIN algorithm,which predicts proteins by constructing active PPI networks through dynamic gene expression.The experimental results proved that our newly proposed similarity coefficient PJC has superior advantages in predicting essential proteins.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.
