A NEW SECOND DERIVATIVE METHODS WITH HYBRID PREDICTORS FOR SOLVING STIFF AND NON-STIFF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This study derives new second derivative linear multistep methods with efficient criteria sufficient for the solvability of the stiff initial value problems by means of interpolation and collocation techniques. The hybrid predictors in the procedure are nested.   The stiff initial value issues in ordinary differential equations were approximated by using power series as the basis function. The method's stability properties were examined and subsequently provided. The region of absolute stability of the novel schemes was studied using the boundary locus method. Through its combination as a block matrix, the resulting approaches are applied to solve a number of stiff initial value issues. The new techniques produced numerical findings and errors that compared favorably with  some existing methods in the literature.