New P-Stable Eighth Algebraic Order Exponentially-Fitted Methods for the Numerical Integration of the Schrodinger Equation

Byline: G. Avdelas (1), E. Kefalidis (2), T.E. Simos (1) Keywords: Schrodinger equation; exponential fitting; P-stability; finite difference; multistep methods; scattering problems Abstract: A family of P-stable high algebraic order exponentially-fitted methods for the numerical solution of the Schrodinger equation is developed in this paper. Numerical illustration to the resonance problem of the radial Schrodinger equation indicates that the new proposed methods are generally more efficient than the previously developed exponentially-fitted methods of the same kind. Author Affiliation: (1) Laboratory of Applied Mathematics and Computers, Department of Sciences, Technical University of Crete, Kounoupidiana, GR-731 00 Chania, Crete, Greece (2) Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-671 00, Xanthi, Greece Article History: Registration Date: 12/10/2004