Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid  

作　　者：Jugal Mohapatra Srinivasan Natesan 

机构地区：[1]Department of Mathematics,Indian Institute of Technology Guwahati,Guwahati-781 039,India

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2010年第1期1-22,共22页高等学校计算数学学报（英文版）

基　　金：supported by the Department of Science & Technology, Government of India under research grant SR/S4/MS:318/06.

摘　　要：Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper, we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function. It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically.

关 键 词：Singular perturbation problems delay differential equations boundary layer upwind scheme adaptive mesh uniform convergence. 

分 类 号：O241.3[理学—计算数学]