TITLE:
Numerical Solution of Quasilinear Singularly Perturbed Problems by the Principle of Equidistribution
AUTHORS:
Quan Zheng, Fulin Ye
KEYWORDS:
Quasilinear Singularly Perturbed BVP, Equidistribution, Adaptive Mesh, Uniform Convergence
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.10,
October
23,
2020
ABSTRACT: In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed.