Basic Concepts in Computational Physics

DOI10.1007/978-3-319-02435-6zbMath1287.65002OpenAlexW4231866009MaRDI QIDQ5891321

Ewald Schachinger, Benjamin A. Stickler

Publication date: 22 November 2013

Full work available at URL: https://doi.org/10.1007/978-3-319-02435-6

zbMATH Keywords

stochastic optimizationnumerical integrationtextbookMarkov chain Monte Carlotwo-body problemMonte Carlo methodsnumerical differentiationSchrödinger equationIsing modelrandom walkmolecular dynamicsstochastic numerical methodsKepler problempseudo random number generatorsdouble pendulumbasic deterministic numerical methodsleast square fitsphase transition fractional integralsPotts model, data analysisrandom splitting methodsRunge-Kutta-4 method

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Monte Carlo methods (65C05) Numerical analysis or methods applied to Markov chains (65C40) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Random number generation in numerical analysis (65C10) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Numerical quadrature and cubature formulas (65D32) Applications to the sciences (65Z05) Numerical differentiation (65D25) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Motion of a rigid body with a fixed point (70E17) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

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The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis ⋮ A ``converse stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation

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