New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems

DOI10.1155/2013/939367zbMath1470.65133OpenAlexW2028087551WikidataQ58917771 ScholiaQ58917771MaRDI QIDQ2319287

Norazak Senu, K. W. Moo, Mohamed Bin Suleiman, Fudziah Bt. Ismail

Publication date: 16 August 2019

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

Full work available at URL: https://doi.org/10.1155/2013/939367

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (5)

One step adapted hybrid second derivative block method for initial value problems with oscillating solutions ⋮ A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems ⋮ Unnamed Item ⋮ Exponentially fitted and trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for solving \(y^{\prime \prime}(x) = f \left(x, y, y^\prime\right)\) ⋮ Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical ivps

Cites Work

• Unnamed Item
• Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
• A phase-fitted Runge-Kutta-Nyström method for the numerical solution of initial value problems with oscillating solutions
• A symplectic Runge-Kutta-Nyström method with minimal phase-lag
• Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s
• A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag
• On the frequency choice in trigonometrically fitted methods
• Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
• New methods for oscillatory problems based on classical codes
• An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
• An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems
• A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution
• A NEW MODIFIED RUNGE–KUTTA–NYSTRÖM METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Solving Ordinary Differential Equations I
• A one-step method for direct integration of structural dynamic equations
• Symmetric Multistip Methods for Periodic Initial Value Problems
• A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS

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