Explicit two-step high-accuracy hybrid methods with minimal phase-lag for \(y^{\prime\prime}= f(x,y)\) and their application to the one-dimensional Schrödinger equation

DOI10.1016/S0377-0427(98)00051-XzbMath0930.65082MaRDI QIDQ1298508

Kaili Xiang, Jian-Jun Zhang

Publication date: 1 February 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationresonancesinterval of periodicityalgebraic order six and eightminimal phase lagmultistep hybrid methods

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 (2)

On the importance of conjugation relations in fractional calculus ⋮ Fractional boundary value problem with \(\psi\)-Caputo fractional derivative

Cites Work

• New variable-step procedure for the numerical integration of the one- dimensional Schrödinger equation
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
• Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y=f(t,y)\)
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
• Coleman's method maximally adapted to the Schrödinger equation
• Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional Schrödinger equation
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• An explicit hybrid method of Numerov type for second-order periodic initial-value problems
• Embedded methods for the numerical solution of the Schrödinger equation
• A generator of high-order embedded \(P\)-stable methods for the numerical solution of the Schrödinger equation
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• A one-step method for direct integration of structural dynamic equations
• Symmetric Multistip Methods for Periodic Initial Value Problems

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