Some new variable-step methods with minimal phase lag for the numerical integration of special second-order initial-value problem

DOI10.1016/0096-3003(94)90139-2zbMath0808.65068OpenAlexW1986461353MaRDI QIDQ1336044

Theodore E. Simos

Publication date: 16 March 1995

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

Full work available at URL: https://doi.org/10.1016/0096-3003(94)90139-2

zbMATH Keywords

Schrödinger equationerror estimatesecond-order initial value problemvariable step methods with minimal phase lag

Mathematics Subject Classification ID

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)

Related Items (7)

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 new family of three-stage two-step P-stable multiderivative methods with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation and IVPs with oscillating solutions ⋮ A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation ⋮ A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods ⋮ High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation ⋮ On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (\(N + 1\)) bodies

Cites Work

• A four-step phase-fitted method for the numerical integration of second order initial-value problems
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• 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
• An explicit almost \(P\)-stable two-step method with phase-lag of order infinity for the numerical integration of second-order periodic initial- value problems
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
• Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• A one-step method for direct integration of structural dynamic equations
• A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problem

This page was built for publication: Some new variable-step methods with minimal phase lag for the numerical integration of special second-order initial-value problem