High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations

Advances in Difference Equations

RK Mohanty¹  Sachin Sharma² 

[1] Department of Applied Mathematics, South Asian University, Chanakyapuri, India;Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India

关键词: quasi-linear parabolic equations;    quasi-variable mesh;    spline in compression;    generalized Burgers-Fisher equations;    coupled Burgers equation;    Newton’s iterative method;    65M06;    65M12;    65M22;    65Y20;   

DOI  :  10.1186/s13662-017-1274-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we propose a new two-level implicit method of accuracy two in time and three in space based on spline in compression approximations using two off-step points and a central point on a quasi-variable mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differential equations. The new method is derived directly from the continuity condition of the first-order derivative of the spline function. The stability analysis for a model problem is discussed. The method is directly applicable to problems in polar systems. To demonstrate the strength and utility of the proposed method, we solve the generalized Burgers-Fisher equation, generalized Burgers-Huxley equation, coupled Burgers-equations and heat equation in polar coordinates. We demonstrate that the proposed method enables us to obtain high accurate solution for high Reynolds number.

【 授权许可】

CC BY