Parameter estimation in exponentially fitted hybrid methods for second order differential problems

DOI10.1007/s10910-011-9903-7zbMath1259.65111OpenAlexW2034597520MaRDI QIDQ424201

Elena Esposito, Raffaele D'Ambrosio, Beatrice Paternoster

Publication date: 31 May 2012

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-011-9903-7

zbMATH Keywords

parameter estimationoscillationnumerical examplessecond-order ordinary differential equationsmolecular dynamicsexponential fittingperidic solutiontwo-step hybrid methods

Mathematics Subject Classification ID

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 (23)

Functionally-fitted block methods for second order ordinary differential equations ⋮ Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods ⋮ Explicit symplectic RKN methods for perturbed non-autonomous oscillators: splitting, extended and exponentially fitting methods ⋮ Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts ⋮ Modified Gauss-Laguerre exponential fitting based formulae ⋮ Exponentially fitted IMEX methods for advection-diffusion problems ⋮ Numerical solution of reaction-diffusion systems of \(\lambda\)-\(\omega\) type by trigonometrically fitted methods ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ Exponentially fitted methods with a local energy conservation law ⋮ Functionally-fitted block \( \theta \)-methods for ordinary differential equations ⋮ Adapted numerical modelling of the Belousov-Zhabotinsky reaction ⋮ Order conditions for general linear Nyström methods ⋮ An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown ⋮ High order exponentially fitted methods for Volterra integral equations with periodic solution ⋮ Runge-Kutta-Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval ⋮ Functionally fitted block method for solving the general oscillatory second-order initial value problems and hyperbolic partial differential equations ⋮ Adapted explicit two-step peer methods ⋮ Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems ⋮ Revised exponentially fitted Runge-Kutta-Nyström methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction of the ef-based Runge-Kutta methods revisited
• Exponentially fitted two-step hybrid methods for \(y^{\prime\prime} = f(x,y)\)
• Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations
• Two-step hybrid collocation methods for \(y^{\prime\prime} = f(x,y)\)
• The optimal exponentially-fitted Numerov method for solving two-point boundary value problems
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• Operations on oscillatory functions
• 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 \(y^{\prime\prime }=f(x,y)\)
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Two Step Runge-Kutta-Nyström Methods for y″ = f(x,y) and P-Stability
• Order conditions for a class of two-step methods for y = f (x, y)
• Truncation Errors in Exponential Fitting for Oscillatory Problems
• Numerical Methods for Ordinary Differential Equations

This page was built for publication: Parameter estimation in exponentially fitted hybrid methods for second order differential problems