Numerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method

Abstract

In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.

A New Iterative Scheme for the Solution of Tenth Order Boundary Value Problems Using First-Kind Chebychev Polynomials

“…In this section we consider the 10 th order boundary value problem of the form (Njoseh and Mamadu, 2016;Viswanadham and Ballem, 2015)…”

“…Thus, several numerical schemes have been developed by many authors for the solution of boundary value problems due to their mathematical significance in diversified applications in science and engineering. For instance, Njoseh and Mamadu (2016), used the power series approximation method for the numerical solution of generalized nth order boundary value problems. Similarly, Mamadu and Njoseh (2016) applied the Tau-collocation approximation approach for solving first and second order ordinary differential equations.…”

An Error Analysis of Implicit Finite Difference Method with Mamadu-Njoseh Basis Functions for Time Fractional Telegraph Equation

“…Problems involving fractional order have equally solved applying these polynomials as seen in the literature Xie [16]. Njoseh and Mamadu [17] applied the MNP as trial functions for the solution of fifth order boundary value problems via the power series approximation method. These polynomials were also used by Mamadu and Njoseh [18] for the solution of Votterra integral equation via the Galerkin Method.…”

Modified Variational Iteration Method with Chebyshev Polynomials for Solving 12th order Boundary Value problems

“…Way development the numerical support of fifth counterfeit ditch profit company permit Mamadu-Njoseh polynomials as grief functions [3]. Token to the talents train guestimate make advances for a outspoken BVP [4]. Including, the path of tau and tau-collocation determine overtures was very much old by Njoseh and Mamadu [5] to have designs on the fill of prime and shoved ordinary differential equations.…”