Abstract
Two two-step methods for the numerical solution of some problems related to the Schrödinger equation are developed in this paper. One is of the Numerov type and of algebraic order 4 and the other is of the Runge-Kutta type and of algebraic order 5. Each of these have free parameters that are defined such that the methods are fitted to spherical Bessel and Neumann functions. From these methods a variable-step technique is devised. This variable-step technique is applied to the phase-shift and resonance problems of the radial Schrödinger equation. Results indicate that the new approach is more efficient than several other well-known methods.
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