AN IMPROVED VERSION OF HOMOTOPY PERTURBATION METHOD FOR MULTI-DIMENSIONAL BURGERS' EQUATIONS

Shweta; Saddam Hussain; Rajesh Kumar; Rajesh Kumar

doi:10.11948/20240143

2025 Volume 15 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(1): 517-546

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Shweta, Saddam Hussain, Rajesh Kumar, Rajesh Kumar. AN IMPROVED VERSION OF HOMOTOPY PERTURBATION METHOD FOR MULTI-DIMENSIONAL BURGERS' EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 517-546. doi: 10.11948/20240143

Citation:

Shweta, Saddam Hussain, Rajesh Kumar, Rajesh Kumar. AN IMPROVED VERSION OF HOMOTOPY PERTURBATION METHOD FOR MULTI-DIMENSIONAL BURGERS' EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 517-546. doi: 10.11948/20240143

AN IMPROVED VERSION OF HOMOTOPY PERTURBATION METHOD FOR MULTI-DIMENSIONAL BURGERS' EQUATIONS

1.
Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan-333031, India
2.
Department of Civil Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan-333031, India

Author Bio: Email: p20210073@pilani.bits-pilani.ac.in(Shweta); Email: p20200438@pilani.bits-pilani.ac.in(S. Hussain); Email: rajesh.kr@pilani.bits-pilani.ac.in(R. Kumar)
Corresponding author: Email: rajesh.kumar@pilani.bits-pilani.ac.in(R. Kumar)

Abstract

Abstract

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.
- Homotopy perturbation method /
- accelerated homotopy perturbation Elzaki transform method /
- Burgers' equation /
- convergence analysis
MSC: 35Q35, 35Q79, 47J05, 49K20

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References

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