A 2-STEP HYBRID BLOCK BACKWARD DIFFERENTIATION FORMULA FOR THE APPROXIMATION OF INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this paper, a two-step hybrid backward differentiation formula, with two off-grid points incorporated at interpolation for the solution of initial value problems of ordinary differential equations is presented. The main method as well as the additional methods are obtained from the same continuous scheme formulated using interpolation and collocation methods with Legendre polynomial as the basis function. The method is seen to be of uniform order k=4. The stability of the proposed method is analyzed and discussed. Numerical experiments were carried out to ascertain the effectiveness of the method in comparison with the approximation produced by some existing methods.