A high order predictor-corrector method for periodic IVPs

DOI10.1016/0893-9659(93)90090-AzbMath0782.65094WikidataQ127216836 ScholiaQ127216836MaRDI QIDQ1312029

Theodore E. Simos

Publication date: 28 February 1994

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

Runge-Kutta methodphase-lagoscillatory solutioninterval of periodicityperiodic initial value problemalgebraic order

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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 (12)

Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions ⋮ A new two-step hybrid method for the numerical solution of the Schrödinger equation ⋮ 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 ⋮ On Numerov's method for a class of strongly nonlinear two-point boundary value problems ⋮ A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions ⋮ A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation ⋮ Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation ⋮ A new symmetric linear eight-step method with fifth trigonometric order for the efficient 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 ⋮ High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation ⋮ A variable mesh C-SPLAGE method of accuracy \(O(k^2h_l^{-1}+kh_l+h_l^3)\) for 1D nonlinear parabolic equations

Cites Work

• A four-step phase-fitted method for the numerical integration of second order initial-value problems
• A Numerov-type method for the numerical solution of the radial Schrödinger equation
• A sixth order predictor-corrector method for periodic IVPs
• Numerov made explicit has better stability
• 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
• Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
• Multiderivative Methods for Periodic Initial Value Problems
• 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
• A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problem
• Symmetric Multistip Methods for Periodic Initial Value Problems

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