Some fourth order multipoint iterative methods for solving equations

Abstract

tion errors of the difference method. Moreover, any error introduced in the nuinerical solution of y' 15 exp [15t] will be damped by exp [14t] in the substitution into (y, t) = y exp [-14t]. Tables 1, 2, 3, and 4 give comparisons of relative errors in the numerical solution of x' 15et 14x obtained by direct integration, versus the solution obtained by using the alternate equationi. The method used is Adams-Bashforth 16th order predictor and Adams-Moulton 15th order corrector. The region of numerical stability (for one application of the corrector) is -.007 < h ? .011. The tables display results using step sizes that caused h to lie both inside (Table 1) and outside (Tables 2, 3, 4) of the stability region for the direct integration. All integrations connected with the solution using the altemate equation are within the stability region.