The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method

DOI10.1155/2013/910624zbMath1275.65044OpenAlexW2084569686WikidataQ58917713 ScholiaQ58917713MaRDI QIDQ370306

D. F. Papadopoulos, Theodore E. Simos

Publication date: 19 September 2013

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/910624

zbMATH Keywords

numerical resultsSchrödinger equationamplification errorfourth algebraic ordermodified Runge-Kutta-Nyström methodphase 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) Error bounds for numerical methods for ordinary differential equations (65L70)

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Cites Work

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• A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation
• A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
• The canonical functions method and singular potentials
• An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems
• An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation
• A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Families of Runge-Kutta-Nystrom Formulae
• Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
• A modified Runge–Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems
• A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS

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