In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.
A. Shokri et al., "Fourth Derivative Singularly P-Stable Method for the Numerical Solution of the Schrödinger Equation," Advances in Difference Equations, vol. 2021, no. 1, article no. 506, SpringerOpen, Dec 2021.
The definitive version is available at https://doi.org/10.1186/s13662-021-03662-9
Mathematics and Statistics
Keywords and Phrases
Consistency; P-Stability; Periodicity; Schrödinger Equation; Singularly P-Stability
International Standard Serial Number (ISSN)
Article - Journal
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01 Dec 2021