Numerical Solution of Higher Order Ordinary Differential Equations by Direct Block Code

Abstract

Problem statement: This study is concerned with the development of a code based on 2-point block method for solving higher order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) directly. Approach: The block method was developed based on numerical integration and using interpolation approach which is similarly as Adams Moulton type. Furthermore, the proposed method is derived in order to solve higher order ODEs in a single code using variable step size and implemented in a predictor corrector mode. This block method will act as simultaneous numerical integrator by computing the numerical solution at two steps simultaneously. Results: The numerical results for the direct block method were superior compared to the existing block method. Conclusion: It is clearly proved that the code is able to produce good results for solving higher order ODEs.