Predictor—Corrector Methods

This chapter elaborates about predictor–corrector methods applicable to ordinary differential equations of the form y′ = f ( x,y ). A sequence of numerical approximations is obtained. One set of predictor–corrector equations is the Adams–Bashforth predictor formula and the Adams–Moulton corrector formula. The corrector formula could be iterated as many times as is necessary to insure convergence; this is called correcting to convergence. In general, if more than two iterations are required, then the step size h is probably too large. The predictor–corrector method is a finite difference scheme that is not a linear multistep method. To obtain the starting values so that the predictor-corrector pair can be used, Runge–Kutta methods can be used.