A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

Zhongcheng Wang and Yongming Dai
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Zhongcheng Wang: Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200436, P. R. China
Yongming Dai: Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200436, P. R. China

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 08, 1087-1105

Abstract: A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

Keywords: Multi-derivative; high-order linear four-step methods; Schrödinger equation; eigenvalue problems; high precision methods (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103005194

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