Some novel efficient numerical methods for solving initial value problems of ordinary differential equations

Abstract

This work is concerned with development, analysis and implementation of some optimized hybrid block methods for solving initial value problems of ordinary differential equations. The development of the proposed methods is based on the theory of interpolation and collocation. Further, the proposed methods have been formulated in adaptive step-size mode by using an embedded-type procedure. Numerical experiments have been carried out on solving some well-known problems by using the proposed methods that demonstrate the good performance of the methods in comparison with some of the well-known existing methods in the literature. newline