Stability and Error Analysis for a Second-Order Fast Approximation of the One-dimensional Schrödinger Equation Under Absorbing Boundary Conditions

DOI10.1137/17M1162111zbMath1412.65119OpenAlexW2903849629MaRDI QIDQ4562337

Buyang Li, Chunxiong Zheng, Jiwei Zhang

Publication date: 19 December 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1162111

zbMATH Keywords

stabilitycomputational complexityexponential sumsnumerical examplesabsorbing boundary conditionSchrödinger equationerror estimateGaussian quadratureconvolution operatorfast algorithmCrank-Nicolson method\(\mathcal{Z}\)-transformfully discrete finite difference scheme

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Schrödinger operator, Schrödinger equation (35J10) Applications to the sciences (65Z05) Numerical integration (65D30)

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Uses Software

• RODAS

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