A New Analytical Approach for Solving Nonlinear Boundary Value Problems Arising in Nonlinear Phenomena

Liaqat Ali, Saeed Islam, Taza Gul, Ali Saleh Alshomrani, Murad Ullah


In this research a new analytical approach is used to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. It converts a complex nonlinear problem into zeroth order and first order problem.
It consists of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The unknown parameters are determined by minimizing the residual. Many methods which are explained in this paper are used to determine these parameters. Here Galerkin's method is used for this purpose. It is applied to solve non-linear BVPs of fourth and fifth order. The results are compared with the already existing methods e.g., Galerkin's Method with Quintic B-splines, Differential Transform Method (DTM), and Optimal Homotopy Asymptotic Method (OHAM). It gives efficient and accurate first-order approximate solution. The results achieved by this technique are in excellent concurrence with the exact solution and hence proved that this method is effective and easy to apply.

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