Predictor Corrector Methods Page 1 Predictor Corrector Methods Predictor Corrector Modes

page 1 Predictor Corrector Methods Predictor Corrector Methods form the basis of the most successful codes (Variable Step Variable Order Methods) for the solution of initial value problems of ordinary differential equations. Briefly, these methods have been successful because they occur in naturally arising families covering a range of orders, they have reasonable stability properties, and they allow for easy error control via suitable step size/order changing policies and techniques. A recent and thorough discussion is in chapter 4 of J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, 1991. This handout extracts some main points from Lambert’s discussion and mostly employs the same notation. Consider the implicit linear multistep method k