Abstract
Two 2-step methods for the numerical solution of some problems of 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 methods have free parameters which will be defined such that the methods are fitted to spherical Bessel and Neumann functions. Based on these methods we have obtained a variable-step method. The results produced based on the phase-shift problem of the radial Schrödinger equation indicate that this new approach is more efficient than other well known methods.
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© 1997 Springer-Verlag Berlin Heidelberg
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Simos, T.E., Williams, P.S. (1997). Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_124
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DOI: https://doi.org/10.1007/3-540-62598-4_124
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