About homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients

TL;DR

This paper critically examines the homotopy perturbation method applied to heat-like and wave-like equations with variable coefficients, revealing that its main results are essentially Taylor expansions and that it demands excessive boundary conditions.

Contribution

The paper provides a critical analysis showing that the homotopy perturbation method's solutions are equivalent to Taylor series and highlights the need for additional boundary conditions.

Findings

Main results are Taylor expansions of exponential and hyperbolic functions.

The method requires more boundary conditions than necessary for power series solutions.

Highlights limitations of the homotopy perturbation method in these models.

Abstract

We analyze a recent application of homotopy perturbation method to some heat-like and wave-like models and show that its main results are merely the Taylor expansions of exponential and hyperbolic functions. Besides, the authors require more boundary conditions than those already necessary for the solution of the problem by means of power series.