MODIFIED HOMOTOPY PERTURBATION METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

Yue Liu; Jing Pang; Yajun Du; Tianle Yin

doi:10.11948/20250011

2025 Volume 15 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(5): 2853-2865

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Yue Liu, Jing Pang, Yajun Du, Tianle Yin. MODIFIED HOMOTOPY PERTURBATION METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2853-2865. doi: 10.11948/20250011

Citation:

Yue Liu, Jing Pang, Yajun Du, Tianle Yin. MODIFIED HOMOTOPY PERTURBATION METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2853-2865. doi: 10.11948/20250011

MODIFIED HOMOTOPY PERTURBATION METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

1.
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
2.
Department of Mathematics and Computer Science, Hetao College, Bayannur 015000, China
3.
Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Hohhot 010051, China

Author Bio: Email: 1072729566@qq.com(Y. Liu); Email: mutujun2022@163.com(Y. J. Du); Email: 3012030050@qq.com(T. L. Yin)
Corresponding author: Email: pang_j@imut.edu.cn(J. Pang)
Fund Project: The authors were supported by National Natural Science Foundation of China (10561151), Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region (JY20220003) and Graduate Research Innovation Project in Inner Mongolia Autonomous Region (B20231102Z)

Abstract

Abstract

Homotopy perturbation method can be widely accepted for approximating or accurately solving nonlinear differential equations due to its generality and ease of use. Rational homotopy perturbation method and Rational biparameter homotopy perturbation method are two extensions of homotopy perturbation method which can improve the accuracy of the solution. In this paper, the algorithm steps of these two derived methods are introduced, meanwhile, the approximate solutions of Burgers equation and Gardner equation are obtained. Absolute errors of these two methods in solving partial differential equations are calculated and described to verify the effectiveness of the methods.
- Rational homotopy perturbation method /
- Rational biparameter homotopy perturbation method /
- approximate solution /
- Burgers equation /
- Gardner equation
MSC: 35C10, 41A58

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References

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