A Three Step Explicit Method for Direct Solution of Third Order Differential Equations

Abstract

This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to the problem is expanded by Taylor series expansion approach. The method is consistent and zero-stable. This is tested on a number of problems to show the accuracy and efficiency. A predictor of y_n+k where K>3 in the main method is also proposed.

Keywords: Linear multistep method, basis function, Taylor series expansion, Predictor, discrete method, Zero stable.