ONE STEP BLOCK HYBRID METHODS FOR THE SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research work, block hybrid methods for solving rst order initial value prob- lems of ordinary di erential equations are proposed. The combination of power series and exponential function are used as an approximate solution for the derivation of the methods in block mode. The methods are derived via interpolation and collocation approaches and the proposed methods are analysed based on the properties of the linear multistep method and the methods are zero-stable, consistent and convergent. The derived methods are tested on real life problems (SIR Model). Six numerical examples are solved to determine the e ciency and accuracy of the derived methods and the numerical solutions obtained yielded better results in term of accuracy when compared with some existing methods in the literature.