Using Optimal Homotopy Asymptotic Method for Solving Differential Equations

Azhar Shareef  Islubi; Muayyad Mahmood  Khalil

Azhar Shareef Islubi Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tirkit, Iraq
Muayyad Mahmood Khalil Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tirkit, Iraq

Keywords: Optimal Homotopy Asymptotic Method, OHAM, Nonlinear differential equations, Semi-analytic methods, Convergence analysis

Abstract

In this study, we address the challenge of solving both linear and nonlinear differential equations by employing the Optimal Homotopy Asymptotic Method (OHAM), a novel semi-analytic approximation technique. Existing methods like the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM) often rely on free parameters, which can limit their effectiveness. OHAM, however, operates without this dependence, achieving higher accuracy with fewer approximations. Through comparative analysis, we demonstrate that OHAM performs consistently well over large domains and allows for easy adjustment of the convergence domain. These findings suggest that OHAM provides a more efficient and accurate alternative for solving complex differential equations.

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