ONE-STEP SECOND DERIVATIVE BLOCK INTRA-STEP METHOD FOR STIFF SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Presented here is a one-step second derivative intra-point block numerical method of uniform order eight for seeking the solution of stiff systems of ordinary differential equations directly. The techniques of interpolation and collocation are used to build the continuous scheme from which the main method and additional methods were obtained. The convergence analysis of the proposed method to validate their effectiveness and reliability is presented. Some numerical examples both linear and non-linear are solved to demonstrate the efficiency of the method.