A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations

CAO Yanhua; ZHANG Zitong; LI Nan

doi:10.21656/1000-0887.420282

Volume 43 Issue 9

Sep. 2022

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CAO Yanhua, ZHANG Zitong, LI Nan. A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations[J]. Applied Mathematics and Mechanics, 2022, 43(9): 1045-1052. doi: 10.21656/1000-0887.420282

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A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations

doi: 10.21656/1000-0887.420282

School of Science, East China Jiaotong University, Nanchang 330013, P.R.China

Received Date: 2021-09-13
Rev Recd Date: 2022-07-08

Available Online: 2022-08-29

Publish Date: 2022-09-30

Abstract

Abstract

As a class of nonlinear partial differential equations, the Burgers equations are widely used in various fields. A new space-time polynomial collocation method was presented for particular solutions to 3D Burgers equations. The basic process was divided into 2 steps. The 1st step is to find the polynomial particular solutions of the linear differential operator terms (including the time differential term) in the governing equation. The 2nd step is to solve the nonlinear term of the 3D Burgers equation iteratively. The proposed method is simple and easy to program. The approximate solution has high accuracy. Especially, the stability of the method is excellent, which improves the programming simplicity and deepens the understanding of high-dimensional Burgers equations and the practical application.
- collocation method,
- polynomial solution method,
- Burgers equation,
- MATLAB program

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References(23)

References

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