Multi-derivative Linear Multi-step Methods for Solving Third Order Boundary Value Problems

Abstract

Multi-derivative linear multi-step methods with continuous coefficients was derived through the block method approach using power series as basis function. Discrete scheme systems involving the multi-derivative linear methods were developed and their basic properties examined. The resulting schemes were used to solve general third order boundary value problems in ordinary differential equations without reducing it to first order. Numerical results were compared with the existing methods to show the accuracy and efficiency of the method. Results obtained show that our methods performed better than the existing methods.