Parameter-robust numerical method for a system of singularly perturbed initial value problems |
| |
Authors: | Sunil Kumar Mukesh Kumar |
| |
Institution: | 1.Department of Mathematics,Indian Institute of Technology Delhi,New Delhi,India;2.Institute of Applied Mathematics and Information Technology-CNR,Pavia,Italy |
| |
Abstract: | In this work we study a system of M( ≥ 2) first-order singularly perturbed ordinary differential equations with given initial conditions. The leading term of
each equation is multiplied by a distinct small positive parameter, which induces overlapping layers. A maximum principle
does not, in general, hold for this system. It is discretized using backward Euler difference scheme for which a general convergence
result is derived that allows to establish nodal convergence of O(N
− 1ln N) on the Shishkin mesh and O(N
− 1) on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical experiments are performed
to support the theoretical results. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|