A CLASS OF HYBRID BLOCK METHODS FOR SOLVING GENERAL FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS OF INITIAL VALUE PROBLEMS

Abstract

This work considers the derivation of two implicit hybrid linear multistep methods for the direct solution of fourth order initial value problems of ordinary di erential equations. The techniques of collocation and interpolation were adopted for the derivation of the methods which were implemented in block mode. The methods were analyzed base on the properties of Linear Multistep Method and were found to be of uniform order ten (10) and twelve (12), consistent, zero stable, hence convergent. The comparison of the results obtained by the derived methods with those of existing methods in literature indicate better performance.This work considers the derivation of two implicit hybrid linear multistep methods for the direct solution of fourth order initial value problems of ordinary di erential equations. The techniques of collocation and interpolation were adopted for the derivation of the methods which were implemented in block mode. The methods were analyzed base on the properties of Linear Multistep Method and were found to be of uniform order ten (10) and twelve (12), consistent, zero stable, hence convergent. The comparison of the results obtained by the derived methods with those of existing methods in literature indicate better performance.