A P-stable hybrid exponentially-fitted method for the numerical integration of the Schrödinger equation

DOI10.1016/S0010-4655(00)00124-7zbMath0982.65080OpenAlexW2014756643MaRDI QIDQ1587752

P. S. Williams, Theodore E. Simos

Publication date: 11 April 2002

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0010-4655(00)00124-7

zbMATH Keywords

numerical experimentsSchrödinger equationfinite difference methodsmultistep methodsexponential fittingresonance problem\(P\)-stability

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (5)

\(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations ⋮ A trigonometrically-fitted method for long-time integration of orbital problems ⋮ Stage reduction on P-stable Numerov type methods of eighth order ⋮ A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems ⋮ A variable step-size exponentially fitted explicit hybrid method for solving oscillatory problems

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