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A higher order uniformly convergent method for singularly perturbed parabolic turning point problems
Author(s) -
Yadav Swati,
Rai Pratima,
Sharma Kapil K.
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22431
Subject(s) - richardson extrapolation , mathematics , discretization , uniform convergence , convergence (economics) , mathematical analysis , a priori and a posteriori , extrapolation , boundary (topology) , logarithm , philosophy , bandwidth (computing) , epistemology , computer science , economics , economic growth , computer network
In this article, we study numerical approximation for a class of singularly perturbed parabolic (SPP) convection‐diffusion turning point problems. The considered SPP problem exhibits a parabolic boundary layer in the neighborhood of one of the sides of the domain. Some a priori bounds are given on the exact solution and its derivatives, which are necessary for the error analysis. A numerical scheme comprising of implicit finite difference method for time discretization on a uniform mesh and a hybrid scheme for spatial discretization on a generalized Shishkin mesh is proposed. Then Richardson extrapolation method is applied to increase the order of convergence in time direction. The resulting scheme has second‐order convergence up to a logarithmic factor in space and second‐order convergence in time. Numerical experiments are conducted to demonstrate the theoretical results and the comparative study is done with the existing schemes in literature to show better accuracy of the proposed schemes.