DERIVATION OF LINEAR MULTISTEP METHODS USING TAYLOR SERIES EXPANSION FOR SOLVING THIRD AND FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this work, Taylor series approach is employed to develop Linear Multistep Methods (LMM) for the solution of third and fourth order ordinary differential equations (ODES). In order to cater for the predictors, Taylor series is still used to handle n j y  and n j f  to the order of accuracy of the particular method under consideration. Analysis of the properties of the methods such as order of accuracy, zero stability, consistency, convergence and region of absolute stability were investigated. The methods developed efficiently solved higher order initial value problems of ordinary differential equation and some real life problems. The results obtained were compared with those obtained by some existing methods. The results of the new methods were found to be better than those generated by some existing methods in terms of accuracy.