A second order fitted operator finite difference scheme for a modified Burgers equation

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Mbroh Nana Adjoah; Noutchie Suares Clovis Oukouomi; Massoukou Rodrigue Yves Mpika

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2021 | Volume:12 | Issue:Special Issue Page(s): 689-698

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Information Journal Paper

Title

A second order fitted operator finite difference scheme for a modified Burgers equation

Author(s)

Mbroh Nana Adjoah | Noutchie Suares Clovis Oukouomi | Massoukou Rodrigue Yves Mpika | Issue Writer Certificate

Keywords

Singularly perturbed problems

Modified Burger's equation

Uniform convergence

Abstract

In this paper, a one-dimensional modified Burgers' equation is considered for different Reynolds numbers. For very high Reynolds numbers, the solution possesses a multiscale character in some part of the independent domain and thus can be classified as a singularly perturbed problem. A numerical scheme that uses a fitted operator finite difference scheme to solve the spatial derivatives and the implicit Euler scheme for the time derivative is proposed to solve the modified Burgers' equation via Rothe's method. It is important to note that the proposed fitted operator finite difference scheme is based on the midpoint upwind scheme. The stability of the scheme is established and the error associated with each discretisation is estimated. Numerical simulations are carried out to validate the theoretical findings.

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