An improved version of homotopy perturbation method for multi-dimensional Burgers’ equations. (English) Zbl 07925061
Summary: The accelerated homotopy perturbation Elzaki transform method (AHPETM), which is based on the homotopy perturbation method (HPM), is used in this article to solve the Burgers equation and system of Burgers equations. AHPETM presents the Elzaki integral transform as a pre-treatment in combination with the decomposition of nonlinear variables to speed up the convergence of the HPM solution to its precise values. When the suggested method’s findings are compared to HPM’s, the results show a considerable improvement. Theoretical convergence analysis and error estimations are also crucial in this work. Multiple numerical examples of 1D, 2D, and 3D Burgers equations, as well as systems of 1D and 2D Burgers equations, are examined to confirm the method’s accuracy. Interestingly, the proposed approach offers the closed-form results to most of the problems, which are essentially the exact solutions.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 47J05 | Equations involving nonlinear operators (general) |
| 49K20 | Optimality conditions for problems involving partial differential equations |
Keywords:
homotopy perturbation method; accelerated homotopy perturbation Elzaki transform method; Burgers’ equation; convergence analysisReferences:
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