Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems

DOI10.1080/00207160.2017.1303138zbMath1499.65280OpenAlexW2593552683MaRDI QIDQ5026492

Jiyong Li, Xuli Qi, Ming Lu

Publication date: 8 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2017.1303138

zbMATH Keywords

order conditionsexplicit methodstrigonometrically fitted methodsmulti-step hybrid methodsoscillatory special second-order initial value problems

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 (4)

Adapted block hybrid method for the numerical solution of Duffing equations and related problems ⋮ One step adapted hybrid second derivative block method for initial value problems with oscillating solutions ⋮ A functionally-fitted block Numerov method for solving second-order initial-value problems with oscillatory solutions ⋮ A two-step modified explicit hybrid method with step-size-dependent parameters for oscillatory problems

Cites Work

• Unnamed Item
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• A new approach on the construction of trigonometrically fitted two step hybrid methods
• Weakly chained diagonally dominant \(B\)-matrices and error bounds for linear complementarity problems
• Exponentially fitted two-step hybrid methods for \(y^{\prime\prime} = f(x,y)\)
• Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs
• General linear methods for \(y^{\prime\prime} = f(y(t))\)
• Extended RKN-type methods for numerical integration of perturbed oscillators
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• Exponentially-fitted and trigonometrically-fitted symmetric linear multistep methods for the numerical integration of orbital problems
• Exponentially fitted Runge-Kutta methods
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Two-step extended RKN methods for oscillatory systems
• Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators
• Exponentially-fitted explicit Runge-Kutta methods
• Error analysis of explicit TSERKN methods for highly oscillatory systems
• A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions
• Scheifele two-step methods for perturbed oscillators
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Chebyshevian multistep methods for ordinary differential equations
• A class of explicit two-step hybrid methods for second-order IVPs
• Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
• EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• Symmetric Multistip Methods for Periodic Initial Value Problems
• On accuracy and unconditional stability of linear multistep methods for second order differential equations
• Order conditions for a class of two-step methods for y = f (x, y)
• EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS
• Mixed collocation methods for \(y=f(x,y)\)

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