Solution of Second-Order Ordinary Differential Equations Through One-Step Hybrid Block Method

Abstract

This study examined the development of the one-step block method for solving second-order initial value problems in ordinary differential equations. The trial function for this method was a Chebyshev interpolating polynomial, and it was developed using the multistep collocation technique. The second derivative of this polynomial served as the collocating equation, and the unknown variables were identified using the Gaussian elimination approach. The order, error-constant, zero stability, consistency, and convergence of the recently suggested approach are all verified. The accuracy of the solution was compared to that of the prior methods and the new strategy outperforms them when used to resolve second-order initial value problems.