Comparison of Block Methods with Different Step-Lengths for Solving Second Order Ordinary Differential Equations

摘要

This article considers the derivation and comparison of block methods with various step-lengths for solving second order initial value problems. The methods were developed via interpolation and collocation approach where a power series was employed as the interpolation equation. The developed methods using different step-lengths were applied to solve second order ordinary differential equations and the numerical solutions were then compared. In general, the results suggested that the higher step-length used, the better accuracy achieved. Further comparison with the existing methods also revealed that these block methods produced better accuracy when solving the same problems.