AN IMPROVED MULTI-DERIVATIVE HYBRID LINEAR MULTISTEP METHODS FOR DIRECT SOLUTION OF THIRDORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This article considered an improved multi-derivative Hybrid linear multistep methods (IMDHLMM) for
direct solution of third-order ordinary differential equations. Power series was used as the basis function
in the derivation of the method. An approximate solution from the basis function was 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 such as order, consistency, zero stability, region of
absolute stability and convergence was tested. The method was implemented in block mode to solve third
order ordinary differential equations inlcuding Genesio equation 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.