In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes...In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.展开更多
This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matri...This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matrix and because of the stability of the M-matrix, it is convergent by the asynchronous iterative method on multiprocessors. Then this paper gives a class of differeifce schemes for linear elliptic PDEs so that their difference matrixes are all M-matrixes and their asynchronous parallel computation are convergent.展开更多
The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes w...The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.展开更多
In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the ex...In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.展开更多
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interfa...In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.展开更多
For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy...For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.展开更多
The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions...The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system展开更多
A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value ...A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.展开更多
In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general fi...In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete w2(2,1)norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.展开更多
The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of...The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2^(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.展开更多
In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic par...In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to the unique generalized solution of the original quasilinear parabolic problem is proved.展开更多
This article computes effect of uniform magnetic field on nanofluid flow filling porous medium inside parallel sheets. Darcy's law is used to characterize porous medium. Flow is caused by stretching of the lower s...This article computes effect of uniform magnetic field on nanofluid flow filling porous medium inside parallel sheets. Darcy's law is used to characterize porous medium. Flow is caused by stretching of the lower sheet. The governing systems are computed using Finite difference technique. This scheme is used due to its more general and powerful nature to solve nonlinear problems. Results are obtained and discussed graphically. Nusselt number, skin friction, streamlines,velocity and temperature are emphasized.展开更多
文摘In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.
文摘This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matrix and because of the stability of the M-matrix, it is convergent by the asynchronous iterative method on multiprocessors. Then this paper gives a class of differeifce schemes for linear elliptic PDEs so that their difference matrixes are all M-matrixes and their asynchronous parallel computation are convergent.
基金Project supported by the National Natural Science Foundation of China and the Foundation of CAEP.
文摘The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.
文摘In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.
基金This work was supported by the Special Funds for Major State Basic Research Projects (Grant No.2005CB321703)the National Natural Science Foundation of China (Grant Nos. 10476002, 60533020)the Science Foundation of CAEP (Grant No. 20060649)
文摘In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.
基金The project is supported by the Special Funds for Major State Basic Research Projects 2005CB321703, the National Nature Science Foundation of China （No. 10476002, 60533020）.
文摘For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.
基金Project supported by the National Natural Science Foundation of China and the Foundation of Chinese Academy of Engineering Physics.
文摘The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
基金This work was supported by China“National Key Program for Developing Basic Sciences”G1999032801the National Natural Science Foundation of China(Grant No.19932010)the Foundation of CAEP(20020652).
文摘A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.
基金The project is supported by China "National Key Program for Developing Basic Sciences" G1999032801 the National Natural Science Foundation of China (No. 19932010)+1 种基金 the National High Technology 863-11 (No.2001AA111040) and the Foundation of CAEP (20
文摘In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete w2(2,1)norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.
基金Project supported by China "National Key Program for Developing Basic Sciences" (No.G1999032801) the National Natural Science Foundation of China (No.19932010) the Science and Technology Foundation of Chinese Academy of Engineering Physics (No.200206
文摘The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2^(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.
基金project is supported by China "National Key Program for Developing Basic Sciences" G1999032801, the National Natural Science Foundation of China (No. 19932010) the National High Technology 863-11 (No.2001AAl 11040) and the Foundation of CAEP (200206
文摘In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to the unique generalized solution of the original quasilinear parabolic problem is proved.
文摘This article computes effect of uniform magnetic field on nanofluid flow filling porous medium inside parallel sheets. Darcy's law is used to characterize porous medium. Flow is caused by stretching of the lower sheet. The governing systems are computed using Finite difference technique. This scheme is used due to its more general and powerful nature to solve nonlinear problems. Results are obtained and discussed graphically. Nusselt number, skin friction, streamlines,velocity and temperature are emphasized.
