### Applications of the homotopy perturbation method for some linear and non-linear partial differential equations

Md. Mizanur Rahman, Md. Masum Murshed, Nasima Akhter

#### Abstract

In this study, some linear PDEs and nonlinear PDEs are investigated using the homotopy perturbation method (HPM). The primary objective of this research is to employ the HPM as a tool for investigating a range of PDEs and extracting their analytical solutions. To clarify the practicality and efficacy of this method, we present illustrative examples of linear PDEs encompassing the classical heat, wave, and Laplace equations. Subsequently, a comparative analysis is performed, contrasting the outcomes derived from the HPM with established accurate solutions. Through this comparative approach, we aim to provide a comprehensive understanding of the HPM's applicability, robustness, and precision in solving a spectrum of PDEs. Our study contributes to the broader exploration of innovative mathematical techniques for tackling complex PDEs, while also shedding light on the potential advantages and limitations of the homotopy perturbation method in practical applications.

#### Keywords

Homotopy Perturbation Method; Partial Differential Equation; Heat equation; Wave equation; Laplace Equation.

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#### References

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DOI: http://dx.doi.org/10.24042/djm.v6i2.17527

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