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- ItemCompact high order finite difference schemes for linear Schrödinger problems on non-uniform meshes(Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Radziunas, Mindaugas; Čiegis, Raimondas; Mirinavičius, AleksasIn the present paper a general technique is developed for construction of compact high-order finite difference schemes to approximate Schrödinger problems on nonuniform meshes. Conservation of the finite difference schemes is investigated. Discrete transparent boundary conditions are constructed for the given high-order finite difference scheme. The same technique is applied to construct compact high-order approximations of the Robin and Szeftel type boundary conditions. Results of computational experiments are presented
- ItemNumerical algorithms for Schrödinger equation with artificial boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Čiegis, Raimondas; Laukaitytė, Inga; Radziunas, MindaugasWe consider a one-dimensional linear Schrödinger problem defined on an infinite domain and approximated by the Crank-Nicolson type finite difference scheme. To solve this problem numerically we restrict the computational domain by introducing the reflective, absorbing or transparent artificial boundary conditions. We investigate the conservativity of the discrete scheme with respect to the mass and energy of the solution. Results of computational experiments are presented and the efficiency of different artificial boundary conditions is discussed.