AI Summary & Key Takeaways
AI InsightAlso, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in literature.
📌 3 Key Takeaways
Abstract
Conventionally, the method of solving fourth order initial value problems of ordinary differential is to first reduce it to a system of first order differential equation. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order and convergence were analyzed. From the analysis, the block method derived was found to be zero stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in literature.