Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order...Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.展开更多
Thermochemical sulfate reduction (TSR) in geological deposits can account for the accumulation of H2S in deep sour gas reservoirs. In this paper, thermal simulation experiments on the reaction of CH4-CaSO4 were carri...Thermochemical sulfate reduction (TSR) in geological deposits can account for the accumulation of H2S in deep sour gas reservoirs. In this paper, thermal simulation experiments on the reaction of CH4-CaSO4 were carried out using an autoclave at high temperatures and high pressures. The products were characterized with analytical methods including carbon isotope analysis. It is found that the reaction can proceed to produce H2S, H2O and CaCO3 as the main products. Based on the experimental results, the carbon kinetic isotope fractionation was investigated, and the value of Ki (kinetic isotope effect) was calculated. The results obtained in this paper can provide useful information to explain the occurrence of H2S in deep carbonate gas reservoirs.展开更多
In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation wi...In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.展开更多
This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation play...This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.展开更多
文摘Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.
文摘Thermochemical sulfate reduction (TSR) in geological deposits can account for the accumulation of H2S in deep sour gas reservoirs. In this paper, thermal simulation experiments on the reaction of CH4-CaSO4 were carried out using an autoclave at high temperatures and high pressures. The products were characterized with analytical methods including carbon isotope analysis. It is found that the reaction can proceed to produce H2S, H2O and CaCO3 as the main products. Based on the experimental results, the carbon kinetic isotope fractionation was investigated, and the value of Ki (kinetic isotope effect) was calculated. The results obtained in this paper can provide useful information to explain the occurrence of H2S in deep carbonate gas reservoirs.
文摘In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.
文摘This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.
