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.
