Solving General and Special Cases of Heat-like Equations with Non Local Conditions Using the Homotopy Perturbation Method
Keywords:
Homotopy perturbation method (HPM), Heat-like equations, Non-local boundary conditions, Partial differential equations.Abstract
This paper presents novel approaches to solving general and special cases of heat-like equations across one and two dimensions, incorporating both initial and non-local boundary conditions. Utilizing the Homotopy Perturbation Method (HPM), we demonstrate the efficacy of this technique in tackling these complex problem sets. Our results show high accuracy, with HPM offering a continuous solution-unlike the discrete approximations provided by finite difference methods. Our findings underscore HPM's potency as a versatile mathematical tool applicable to a wide array of linear and nonlinear problems spanning various scientific and technological domains.
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