Boundary Value Method for Numerically Solving Fifth-order Boundary Value Problems

In this work, fifth-order Boundary-Value Problems (BVPs) in Ordinary Differential Equation are solved numerically using Boundary Value Method. Continuous linear multistep methods are developed with continuous coefficients. This constitutes appropriate methods termed the main and additional methods, which are applied sequentially in blocks to approximate the solution. The method is shown to be flexible in handling linear and nonlinear fifth order BVPs. The convergence of the method is discussed. Several numerical examples are shown to illustrate the superiority of the method developed as the approximate solutions derived from the method are compared to the exact solutions of the problem, and other methods from existing literature.