Optimization of one-step hybrid method for direct solution of fifth order ordinary differential equations of initial value problems

This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing order introduction six-hybrid points for direct solution fifth ordinary differential equations initial value problems (IVPs). Power series was used as basis function IVP. The interpolated at some selected whereas derivative approximate collocated all interval integration to generate system linear determination unknown parameters. derived tested consistency, zero stability, convergence absolute stability. with two test confirm its accuracy usability. comparison results existing methods shows superiority method.