This article is cited in 3 papers

Fourth-order numerical scheme based on half-step nonpolynomial spline approximations for 1D quasi-linear parabolic equations

R. K. Mohanty^a, S. Sharma<sup>b

a</sup> Department of Applied Mathematics, Faculty of Mathematics and Computer Science, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi 110021, India
^b Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India

Abstract: In this article, we discuss a fourth-order accurate scheme based on non-polynomial spline in tension approximations for the solution of quasi-linear parabolic partial differential equations. The proposed numerical method requires only two half-step points and a central point on a uniform mesh in the spatial direction. This method is derived directly from a continuity condition of the first-order derivative of a non-polynomial tension spline function. The stability of the scheme is discussed using a model linear PDE. The method is directly applicable to solving singular parabolic problems in polar systems. The proposed method is tested on the generalized Burgers–Huxley equation, the generalized Burgers–Fisher equation, and Burgers' equations in polar coordinates.

Key words: quasi-linear parabolic equations, spline in tension, generalized Burgers–Huxley equation, generalized Burgers–Fisher equation, Newton's iterative method.

MSC: Primary 65M06, 65M12, 65M22; Secondary 65Y20

Received: 14.12.2018
Revised: 01.02.2019
Accepted: 15.10.2019

 English version: Numerical Analysis and Applications, 2020, 13:1, 68–81

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