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Engineering with Computers
Published in: Engineering with Computers 4/2021

28-02-2020 | Original Article

A new high-accuracy method based on off-step cubic polynomial approximations for the solution of coupled Burgers’ equations and Burgers–Huxley equation

Authors: R. K. Mohanty, Sachin Sharma

Published in: Engineering with Computers | Issue 4/2021

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Abstract

Using two off-step points and a central point, we discuss a new two-time-level implicit method of order three based on polynomial cubic spline approximations for the solution of the system of 1D nonlinear parabolic equations on a quasi-variable mesh. The proposed method is derived directly from the consistency condition. The stability analysis for a model problem is discussed. The proposed method is tested to solve the coupled Burgers’ equations and Burgers–Huxley equation to demonstrate the utility of the method. We show that the proposed method enables us to obtain the high-accurate numerical solution for high Reynolds number.
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Metadata
Title
A new high-accuracy method based on off-step cubic polynomial approximations for the solution of coupled Burgers’ equations and Burgers–Huxley equation
Authors
R. K. Mohanty
Sachin Sharma
Publication date
28-02-2020
Publisher
Springer London
Published in
Engineering with Computers / Issue 4/2021
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-020-00982-4

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