Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations

DOI10.1016/j.matcom.2010.10.011zbMath1210.65133OpenAlexW2076112815MaRDI QIDQ631239

M. Ferro, Beatrice Paternoster, Raffaele D'Ambrosio

Publication date: 22 March 2011

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2010.10.011

zbMATH Keywords

stabilitynumerical experimentspolynomial fittingtrigonometrical fittingsecond order ordinary differential equationstwo-step hybrid methodsoscillatory or periodic solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Uses Software

• RODAS

Cites Work

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• Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies
• Stability of collocation-based Runge-Kutta-Nyström methods
• Two-step hybrid collocation methods for \(y^{\prime\prime} = f(x,y)\)
• Two-step almost collocation methods for ordinary differential equations
• Exponentially-fitted Numerov methods
• On a new type of mixed interpolation
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• A phase-fitted collocation-based Runge-Kutta-Nyström method
• Frequency evaluation in exponential fitting multistep algorithms for ODEs
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Exponentially-fitted explicit Runge-Kutta methods
• Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
• Collocation–Based Two Step Runge–Kutta Methods for Ordinary Differential Equations
• Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• A New Theoretical Approach to Runge–Kutta Methods
• Order conditions for a class of two-step methods for y = f (x, y)
• P-stability and exponential-fitting methods for y = f(x,y)
• A General Family of Two Step Collocation Methods for Ordinary Differential Equations
• Truncation Errors in Exponential Fitting for Oscillatory Problems
• Mixed collocation methods for \(y=f(x,y)\)

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