A PARAMETER-UNIFORM TAILORED FINITE POINT METHOD FOR SINGULARLY PERTURBED LINEAR ODE SYSTEMS＊  

作　　者：Houde Han J.J.H. Miller Min Tang 

机构地区：[1]Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China [2]Department of Mathematics, Trinity College, Dublin 2, Ireland [3]Key Laboratory of Scientific and Engineering Computing, Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

出　　处：《Journal of Computational Mathematics》2013年第4期422-438,共17页计算数学（英文）

基　　金：Acknowledgments. H. Han was supported by the NSFC Project No. 10971116. M. Tang is supported by Natural Science Foundation of Shanghai under Grant No. 12ZR1445400.

摘　　要：In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes. In this work, we consider an initial-final value problem for a multi-scale singularly perturbed system of linear ordi- nary differential equations with discontinuous coefficients. We construct a tailored finite point method, which yields approximate solutions that converge in the maximum norm, uniformly with respect to the singular perturbation parameters, to the exact solution. A parameter-uniform error estimate in the maximum norm is also proved. The results of numerical experiments, that support the theoretical results, are reported.In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes. In this work, we consider an initial-final value problem for a multi-scale singularly perturbed system of linear ordi- nary differential equations with discontinuous coefficients. We construct a tailored finite point method, which yields approximate solutions that converge in the maximum norm, uniformly with respect to the singular perturbation parameters, to the exact solution. A parameter-uniform error estimate in the maximum norm is also proved. The results of numerical experiments, that support the theoretical results, are reported.

关 键 词：Tailored finite point method Parameter uniform Singular perturbation ODEsystem. 

分 类 号：O241.81[理学—计算数学] O231[理学—数学]