A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

DOI10.1007/s10910-012-0035-5zbMath1310.65079OpenAlexW2081127828MaRDI QIDQ1930501

Ibraheem Alolyan, Theodore E. Simos

Publication date: 11 January 2013

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-012-0035-5

zbMATH Keywords

numerical exampleserror boundSchrödinger equationphase-lagmultistep methodshybrid methodsderivatives of the phase-laginterval of periodicityphase-fitted\(P\)-stability

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

A new optimized Runge-Kutta pair for the numerical solution of the radial Schrödinger equation ⋮ THDRK methods with vanished phase-lag and its first derivative for the Schrödinger equation ⋮ Trigonometrically fitted two-step Obrechkoff linear methods for the Schrödinger equation ⋮ Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives ⋮ Algorithm for the development of families of numerical methods based on phase-lag Taylor series

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