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
Citation: 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

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

doi: 10.21656/1000-0887.420282
  • Received Date: 2021-09-13
  • Rev Recd Date: 2022-07-08
  • Available Online: 2022-08-29
  • Publish Date: 2022-09-30
  • 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.

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