An explicit hybrid method of Numerov type for second-order periodic initial-value problems

DOI10.1016/0377-0427(94)00011-OzbMath0844.65061MaRDI QIDQ1899970

J. M. Franco

Publication date: 29 August 1996

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

zbMATH Keywords

algorithmperiodic solutionsnumerical examplesexplicit hybrid methodfourth-order four stage Numerov methodsecond-order periodic initial-value problemssymplectic integrations

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 (19)

Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations ⋮ SDIRK methods for stiff ODEs with oscillating solutions ⋮ Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems ⋮ An adapted explicit hybrid method of Numerov-type for the numerical integration of perturbed oscillators ⋮ Unnamed Item ⋮ Unnamed Item ⋮ 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 ⋮ Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation ⋮ Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations ⋮ A mono-implicit Runge-Kutta-Nyström modification of the Numerov method ⋮ High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic initial value problems ⋮ Zero-dissipative phase-fitted hybrid methods for solving oscillatory second order ordinary differential equations ⋮ Trigonometric symmetric boundary value method for oscillating solutions including the sine-Gordon and Poisson equations ⋮ A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation ⋮ 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 ⋮ Two-step explicit methods for second-order IVPs with oscillatory solutions ⋮ A class of explicit two-step hybrid methods for second-order IVPs ⋮ A phase-fitted collocation-based Runge-Kutta-Nyström method ⋮ A new type of hybrid multistep multiderivative formula for solving stiff IVPs

Uses Software

• ODEPACK

Cites Work

• Unnamed Item
• Order conditions for canonical Runge-Kutta-Nyström methods
• Symplectic integrators and their application to dynamical astronomy
• High-order P-stable multistep methods
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
• Numerov made explicit has better stability
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• Chawla-Numerov method revisited
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Damping and phase analysis for some methods for solving second-order ordinary differential equations
• Symmetric Multistip Methods for Periodic Initial Value Problems

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