SELF-STARTING BLOCK METHODS FOR SOLVING INITIAL VALUE PROBLEMS OF THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This work centers on the development, analysis and implementation of 3-step, 4-step, and 5-step block methods for solving third order initial value problems of ordinary differential equations. The derivation is achieved using power series as basis function by adopting interpolation and collocation of some grid points to obtain a system of linear equations. The system of linear equations is solved using Gaussian elimination method to obtain the unknown coefficients.The coefficients generated are substituted into the approximate solution to obtain a continuous scheme. The first and second derivatives of the continu- ous scheme are evaluated at some grid points to generate members of the proposed block method. Taylor series expansion was adopted, to estimate the order and error constant of the schemes. The methods were shown to be consistent and zero stable, hence conver- gent. The derived methods were applied on third order initial value problem of ordinary differential equations. Error comparison was also made with some existing methods in literature and it was found out that the derived schemes compared favorably with them.