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 Schrödinger equation is developed in this paper. Since the method is P-stable (i.e., its interval of periodicity is equal to (0,∞), 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 Schrödinger equation show the efficiency of the developed method.

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