Kwok, Yue-Kuen; Barthez, Daniel Padé and upwinding finite difference schemes for the quantum mechanical equation of motion. (English) Zbl 0744.65093 Commun. Appl. Numer. Methods 7, No. 8, 639-647 (1991). This paper presents a systematic approach to search for a two-level six- point finite difference of Padé type for the numerical solution of the quantum mechanical equation of motion. Convergence and stability, properties are also analyzed. It is shown that Padé schemes are unconditionally stable. Reviewer: P.K.Mahanti (Ranchi) MSC: 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q40 PDEs in connection with quantum mechanics Keywords:finite difference; quantum mechanical equation of motion; Convergence; stability; Padé schemes PDFBibTeX XMLCite \textit{Y.-K. Kwok} and \textit{D. Barthez}, Commun. Appl. Numer. Methods 7, No. 8, 639--647 (1991; Zbl 0744.65093) Full Text: DOI References: [1] Warming, J. Comput. Phys. 14 pp 159– (1974) [2] Numerical Solutions of Partial Differential Equations: Finite Difference Methods, 3rd edn, Oxford University Press, 1985. [3] and , The Finite Difference Method in Partial Differential Equations, Wiley, 1980. [4] Chattaraj, J. Comput. Phys. 72 pp 504– (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.