High-order methods with minimal phase-lag for the numerical integration of the special second-order initial value problem and their application to the one-dimensional Schrödinger equation

DOI10.1016/0010-4655(93)90106-MzbMath0855.65085OpenAlexW2011318476MaRDI QIDQ1923711

Theodore E. Simos

Publication date: 20 February 1997

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

Full work available at URL: https://doi.org/10.1016/0010-4655(93)90106-m

zbMATH Keywords

Schrödinger equationinterval of periodicityresonance problemsecond-order initial value problemNumerov methodtwo-step sixth-order methods with phase-lag

Mathematics Subject Classification ID

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

Related Items (4)

ADM‐WENO scheme and its application in compressible mixing flows ⋮ High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation ⋮ Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation ⋮ A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

Cites Work

• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• High-accuracy P-stable Methods for y^″ = f(t, y)
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• A one-step method for direct integration of structural dynamic equations

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