Browsing by Author "Alade, Yusuf Aduragba"

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    Mahgoub Homotopy Analysis Method for the Solutions of Nonlinear Ordinary and Partial Differential Equations
    (University of Ilorin, Nigeria., 2026-03-10) Yisa, Babatunde Morufu; Alade, Yusuf Aduragba
    Solving nonlinear problems involving both partial and ordinary differential equations is always more involving and mostly impossible through the well-established traditional analytical methods. We therefore proposed an analytical method that is derived through exploiting Mahgoub transform that is capable of solving variable coefficient linear differential equations. But this transform being unable to solve nonlinear problem, informed the integration of Homotopy analysis method to handle the nonlinear part. Thus, Mahgoub Homotopy Analysis Method (MHAM) that is proposed reduces the volume of computation as well as producing the exact solution of the problem considered. Mahgoub of all the terms in the given equation is taken, and most importantly the differential coefficient. The Mahgoub terms independent of nonlinear term constitute the initial approximation, while the recurrence relation is developed by using the nonlinear terms. The two important deformation equations in the HAM are therefore obtained. The final solution is arrived at via taking the inverse Mahgoub of terms. Few questions on both ordinary and partial differential equations are used to validate the proposed method. The coding and general computations are carried out via Mathematica 13.3.