By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Singl...By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.展开更多
In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for th...In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.展开更多
基金Science and Engineering Research Board(DST,Govt.of India)Grant No.SR/FTP/MS-020/2011Chinese Academy of Sciences President’s International Fellowship Initiative,Grant No.2015PM034。
文摘By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.
基金The first author was supported by Hungarian National Research Fund OTKA No.K67819the second author was partially supported by Hungarian National Research Fund OTKA No.K67819the first and the third authors were supported by Jedlik project “ReCoMend”2008-2011。
文摘In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.
