DEVELOPMENT OF BLOCK HYBRID BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING CLASS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research, the Block Hybrid Backward Differentiation Formulae (BHBDF) for the step number K= 4,5 and 6 were developed for the solution of general second order ordinary differential equations ODE. The Order of the Block methods are 5,6 and 7 respectively. The Continuous formulations of this methods were done through interpolation and collocation approaches. The power series polynomial was used as basis function at some selected grids and off-grids points. The continuous schemes were further evaluated at those points to produce discrete schemes which are combined to form block method. Analysis of the basic properties of the discrete schemes investigated showed consistency, zero stability and convergence of the proposed block methods. Numerical examples were solved to examine the efficiency and accuracy of the proposed method. The results showed that the proposed methods with relatively small errors performed favorably in comparison with the existing methods.