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Numerical Solution of the Burgers Equation

Chee Tiong Ong, Yee Ming Chew, Kim Gaik Tay

Open publisher page 6 citations

Abstract

This is a chapter on numerical solutions of the Burgers equation given by Ut + eUUx - ? Uxx = 0, a = x = b. The Burgers equation is a nonlinear partial di?erential equations which combines the e?ect of nonlinearity (eUUx) and dissipation (? Uxx). Even though there is an analytical solution for the Burgers equation, we certainly look for other alternative to solve the Burgers equation. The semi-implicit pseudo-spectral method is used to develop a numerical scheme to solve the Burgers equation with Gaussian type initial condition. The numerical simulation is carried out using a numerical solver (FORSO) and shown to be consistent with previous studies

About this research paper

What this paper is about

This is a chapter on numerical solutions of the Burgers equation given by Ut + eUUx - ? Uxx = 0, a = x = b. The Burgers equation is a nonlinear partial di?erential equations which combines the e?ect of nonlinearity (eUUx) and dissipation (? Uxx). Even though there is an analytical solution for the Burgers equation, we certainly look for other alternative to solve the Burgers equation. The semi-implicit pseudo-spectral method is used to develop a numerical scheme to solve the Burgers equation with Gaussian type initial condition. The numerical simulation is carried out using a numerical solver (FORSO) and shown to be consistent with previous studies

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This is a chapter on numerical solutions of the Burgers equation given by Ut + eUUx - ? Uxx = 0, a = x = b. The Burgers equation is a nonlinear partial di?erential equations which combines the e?ect of nonlinearity (eUUx) and dissipation (? Uxx). Even though there is an analytical solution for the Burgers equation, we certainly look for other alternative to solve the Burgers equation. The semi-implicit pseudo-spectral method is used to develop a numerical scheme to solve the Burgers equation with Gaussian type initial condition. The numerical simulation is carried out using a numerical solver (FORSO) and shown to be consistent with previous studies

Key concepts: Burgers' equation, Mathematics, Nonlinear system, Mathematical analysis, Kadomtsev–Petviashvili equation, Solver, Dissipation, Numerical analysis

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