Approximating non linear higher order ODEs by a three point block algorithm

Abstract

Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods were introduced to approximate the solutions. Initially when developing a numerical algorithm, researchers focused on the key aspect which is accuracy of the method. As numerical methods becomes more and more robust, accuracy alone is not sufficient hence begins the pursuit of efficiency which warrants the need for reducing computational cost. The current research proposes a numerical algorithm for solving initial value higher order ordinary differential equations (ODEs). The proposed algorithm is derived as a three point block multistep method, developed in an Adams type formulae (3PBCS) and will be used to solve various types of ODEs and systems of ODEs. Type of ODEs that are selected varies from linear to nonlinear, artificial and real life problems. Results will illustrate the accuracy and efficiency of the proposed three point block method. Order, stability and convergence of the method are also presented in the study.