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A generalization of Numerov’s method for the numerical solution of the Schrödinger equation in two dimensions. (English) Zbl 1046.65092
Summary: Generalizations of the well known Numerov’s method are obtained. The local truncation errors of the new methods are presented and the result of the application of the new methods to a two-dimensional Schrödinger equation in an equal space discretization is presented. Numerical illustrations show the efficiency of the new methods compared with the known five-point formula in two Coulomb potentials.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
65N15 Error bounds for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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