Ashyralyev, Allaberen; Hicdurmaz, Betul On the numerical solution of fractional Schrödinger differential equations with the Dirichlet condition. (English) Zbl 1255.65156 Int. J. Comput. Math. 89, No. 13-14, 1927-1936 (2012). Summary: The first and second orders of accuracy difference schemes for the mixed problem for the multidimensional fractional Schrödinger differential equation with dependent coefficients are considered. Stability estimates for solutions of these difference schemes are obtained. Numerical methods are proposed for solving the one-dimensional fractional Schrödinger differential equation with Dirichlet condition in the space variable. Cited in 19 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35R11 Fractional partial differential equations Keywords:difference scheme; fractional Schrödinger differential equation; Dirichlet condition; fractional differential equation; stability PDFBibTeX XMLCite \textit{A. Ashyralyev} and \textit{B. Hicdurmaz}, Int. J. Comput. Math. 89, No. 13--14, 1927--1936 (2012; Zbl 1255.65156) Full Text: DOI References: [1] DOI: 10.1016/S0960-0779(03)00339-4 · Zbl 1053.81027 [2] Adda F. B., Acta Math. Acad. Sci. Hung. 161 pp 323– (2005) [3] DOI: 10.1016/j.jmaa.2009.04.012 · Zbl 1175.26004 [4] DOI: 10.1016/j.aml.2011.02.002 · Zbl 1217.34006 [5] DOI: 10.1155/2009/730465 · Zbl 1184.65083 [6] DOI: 10.1016/j.amc.2010.11.017 · Zbl 1221.65212 [7] DOI: 10.1108/03684921111142287 [8] DOI: 10.1016/j.camwa.2007.04.021 · Zbl 1155.65368 [9] DOI: 10.1016/j.na.2009.05.048 · Zbl 1239.65053 [10] DOI: 10.1155/2009/824385 · Zbl 1190.65185 [11] DOI: 10.1007/s10625-005-0205-3 · Zbl 1081.35004 [12] Kilbas A. A., Theory and Applications of Fractional Differential Equations (2006) · Zbl 1138.26300 [13] DOI: 10.1103/PhysRevE.62.3135 [14] DOI: 10.1016/S0375-9601(00)00201-2 · Zbl 0948.81595 [15] DOI: 10.1103/PhysRevE.66.056108 [16] DOI: 10.1137/1018042 · Zbl 0324.44002 [17] Naber M., J. Math. Phys. 45 (7) pp 18– (2004) [18] DOI: 10.1088/1742-6596/96/1/012066 [19] Podlubny I., Fractional Differential Equations (1999) · Zbl 0924.34008 [20] DOI: 10.1016/j.physleta.2007.06.071 · Zbl 1217.81068 [21] Sobolevskii P. E., Difference Methods for the Approximate Solution of Differential Equations (1975) [22] DOI: 10.1142/S0129167X07004102 · Zbl 1119.26011 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.