A family of P-stable eighth algebraic order methods with exponential fitting facilities

A P-stable exponentially-fitted method of algebraic order eight for the approximate numerical integration of the Schrodinger equation is developed in this paper. Since the method is P-stable (i.e., its interval of periodicity is equal to (0, infinity), large stepsizes for the numerical integration can be used. Based on this new method and on a sixth algebraic order exponentially-fitted P-stable method developed by Simos and Williams [1], a new variable step method is obtained. Numerical results presented for the coupled differential equations arising from the Schrodinger equation show the efficiency of the developed method.