A Numerical Comparison Between the Standard and Modified Versions of the Optimal Homotopy Asymptotic Method (OHAM) for Solving Volterra Integro-Delay Differential Equations (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we formulate and enhance a robust semi-analytical method, known as the Optimal Homotopy Asymptotic Method (OHAM), for solving Volterra delay integro-differential equations (VDIDEs). A comparative analysis between the standard OHAM and its modified version is presented, emphasizing the improvements introduced through the modification. The modificationis based on a refined construction of the auxiliary function H(p), which plays a crucial role in enhancing both the accuracy and the convergence of the method. The effectiveness and efficiency of the proposed technique are demonstrated through the solution of various numerical problems. Notably, the modified OHAM achieves higher accuracy within a single order of iteration, in contrast to the four orders required by the standard OHAM. This advancement significantly reduces computational effort, simplifies calculations, and decreases overall time consumption, thereby establishing the modified OHAM as a more efficient and practical tool for addressing such equations.
Keywords: Nonlinear Delay Voltera Integro-Differential Equations; Laplace Transform, Pade Approximants.