Runge-Kutta method with equation dependent coefficients

DOI10.1016/j.cpc.2011.08.017zbMath1263.65074OpenAlexW2105748997MaRDI QIDQ1947066

L. Gr. Ixaru

Publication date: 12 April 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2011.08.017

zbMATH Keywords

linear stabilitynumerical exampleserror analysisRunge-Kutta methodexponential fitting

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (16)

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ Two-step peer methods with equation-dependent coefficients ⋮ Modified Gauss-Laguerre exponential fitting based formulae ⋮ Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ Frequency evaluation for adapted peer methods ⋮ A stable and accurate scheme for nonlinear diffusion equations: application to atmospheric boundary layer ⋮ Novel exponentially fitted two-derivative Runge-Kutta methods with equation-dependent coefficients for first-order differential equations ⋮ Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems ⋮ Runge-Kutta-Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval ⋮ A new family of A-stable Runge-Kutta methods with equation-dependent coefficients for stiff problems ⋮ Adapted explicit two-step peer methods ⋮ Exponential and trigonometrical fittings: user-friendly expressions for the coefficients ⋮ Revised exponentially fitted Runge-Kutta-Nyström methods

Uses Software

• RODAS

Cites Work

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• Construction of the ef-based Runge-Kutta methods revisited
• Exponentially fitted variable two-step BDF algorithm for first order ODEs
• Exponential fitting BDF-Runge-Kutta algorithms
• Second-order stabilized explicit Runge-Kutta methods for stiff problems
• On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods.
• Trees and numerical methods for ordinary differential equations
• Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
• 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
• Exponential fitted Runge-Kutta methods of collocation type: Fixed or variable knot points?
• Frequency evaluation in exponential fitting multistep algorithms for ODEs
• Exponentially fitted Runge-Kutta methods
• An embedded pair of exponentially fitted explicit Runge-Kutta methods
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Exponentially-fitted explicit Runge-Kutta methods
• Frequency evaluation for exponentially fitted Runge-Kutta methods
• A family of A-stable Runge Kutta collocation methods of higher order for initial-value problems
• A functional fitting Runge-Kutta method with variable coefficients
• Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods

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