A Fitted Numerov Method for Singularly Perturbed Parabolic Partial Differential Equation with a Small Negative Shift Arising in Control Theory
作者机构：Department of MathematicsVisvesvaraya National Institute of TechnologyNagpur440010India
出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)
年 卷 期：2014年第7卷第1期
页 面：23-40页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：The authors wish to thank the Department of Science&Technology Government of India for their financial support under the project No.SR/S4/MS:598/09
主 题：Singular perturbations parabolic partial differential equation exponentially fitted method differential-difference equations
摘 要：In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal *** boundary value problems are associated with a furnace used to process a metal sheet in control ***,the study focuses on the effect of shift on the boundary layer behavior of the solution via finite difference *** the shift parameter is smaller than the perturbation parameter,the shifted term is expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is *** proposed finite difference scheme is unconditionally *** the shift parameter is larger than the perturbation parameter,a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted scheme is *** scheme is also unconditionally *** applicability of the proposed methods is demonstrated by means of two examples.
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