AN EXPLICIT MODIFIED MULTISTEP METHOD FOR THE NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS

摘要

It has been shown by Dahlquist that the maximum order of a stable linear multistep method for the numerical integration of an ordinary differential equation is k+2. It is also known that extreme difficulty is encountered while attempting to achieve high orders with methods of the Runge-Kutta type. By the addition of one term to the linear multistep method, Gragg and Stetter introduced a new class of methods which combine the Runge-Kutta and multistep ideas. Butcher has given explicit formulas for the case of two predictors and one corrector formula and attained an order of 2k+l.nThe purpose of this thesis is to exhibit explicit formulas for the case of one predictor and one corrector formula. It is shown that this method has order 2k. The difference operators for the predictor, corrector, and combined formulas are exhibited.