A Class of Hybrid Multi-derivative linear multistep methods for direct solving third-order ordinary differential equations

Abstract

This article considered a Class of Hybrid Multi-derivatve Linear Multistep Method (CHMLMM) for solving third-order ordinary differential equations. Power series was adopted as the basis function to derive the method. In order to get a desired solution, the basis function was approximated and interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The basic properties of the method were examined. The derived method was implemented in block mode to solve third-order ordinary differential equations to demonstrate the usability and efficiency of the methods. The absolute error obtained in the numerical experiments showed a better performance of the present method over some of the existing methods in the literature.