ONE-STEP SECOND DERIVATIVE BLOCK INTRA-STEP POINTS FOR STIFF SYSTEMS OF INITIAL VALUE PROBLEMS

Abstract

Modified class of single-step numerical schemes were proposed to improve the order of accuracy by imposing intra-step points in the formulation process of the proposed algorithms. The behaviour of modified numerical algorithm is of great concern when varieties of countable off-grid points are imposed within the grid points in the derivation process. In this study, we present a one-step second derivative modified algorithms for numerical solution of first order initial value problems of ODEs. The consistency, convergence and order of accuracy of the algorithms are improved by interpolating and collocating the power series polynomials at carefully selected intra points generated by the Bhaskara cosine formula. The proposed methods are self starting and applied as simultaneous numerical integrators on non-overlapping intervals. In order to further illustrate the effectiveness of the proposed algorithms, stiff systems of IVPs are considered and results obtained are compared with those from related schemes and other methods in the literature.