LEGEND RE-FITTED LINEAR MULTI-STEP METHODS FOR GENERAL FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research, Legendre-fitted Linear Multistep Methods (LLMMs) for general fourth order Ordinary Differential Equations (ODEs) were developed and implemented in predictorcorrector mode. In the derivation, Legendre polynomials was used as the basis function. Collocation and interpolation points are considered at selected grid points. The continuous methods obtained were evaluated at the last grid point of each of the intervals. The resulting systems of equation were solved for the unknown parameters and the values of the unknown parameters were substituted in the approximate solution to obtain the required methods after simplification. The developed methods were tested and found to be consistent, stable and convergent. Accuracy of the methods were compared with the existing methods, and the results showed that it performed better than the existing methods in terms of accuracy.