IMPLICIT FOUR-STEP APPROACH WITH APPLICATION TO NON-LINEAR THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

A unique and efficient implicit four-step approach with application to nonlinear third order ordinary differential equations is considered in this article. In the derivation of this method Collocation and Interpolation techniques were engaged and power series approximate solution was used as the interpolating polynomial. The third derivative of the power series was collocated at the entire grid points, while the interpolation was done at the first three points. Appropriate study of the basic properties of the method was done. The results generated when the new block method was applied on nonlinear third order ordinary differential equations are better in terms of accuracy than the existing methods.