Highly stable Runge-Kutta methods for Volterra integral equations

DOI10.1016/j.apnum.2012.03.007zbMath1243.65157OpenAlexW2062314616MaRDI QIDQ425368

C. Chiapparelli, Giuseppe Izzo, Elvira Russo

Publication date: 8 June 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.03.007

zbMATH Keywords

numerical exampleslinear stability analysisRunge-Kutta methodsnonlinear Volterra integral equations\(V_{0}(\alpha )\)-stability\(V_{0}\)-stabilityconvolution test equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Volterra integral equations (45D05)

Related Items (9)

Numerical methods based on the Floater-Hormann interpolants for stiff VIEs ⋮ Natural Volterra Runge-Kutta methods ⋮ Construction of efficient general linear methods for stiff Volterra integral equations ⋮ Highly stable multistep Runge-Kutta methods for Volterra integral equations ⋮ Generalized linear multistep methods for ordinary differential equations ⋮ A multistep Legendre pseudo-spectral method for nonlinear Volterra integral equations ⋮ General linear methods with large stability regions for Volterra integral equations ⋮ On the error analysis of the numerical solution of linear Volterra integral equations of the second kind ⋮ Pouzet-Runge-Kutta-Chebyshev method for Volterra integral equations of the second kind

Uses Software

• fminsearch

Cites Work

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• General linear methods for Volterra integral equations
• Stability analysis of methods employing reducible rules for Volterra integral equations
• Highly stable parallel Volterra Runge-Kutta methods
• Two-step almost collocation methods for Volterra integral equations
• Advances on Collocation Based Numerical Methods for Ordinary Differential Equations and Volterra Integral Equations
• The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods
• Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind and Their Applications
• Convergence and Stability Analysis for Modified Runge—Kutta Methods in the Numerical Treatment of Second-Kind Volterra Integral Equations
• On the Numerical Stability of Reducible Quadrature Methods for Second Kind Volterra Integral Equations
• Convergence and stability results in Runge-Kutta type methods for Volterra integral equations of the second kind
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
• Modified Multilag Methods for Volterra Functional Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Stability Regions in the Numerical Treatment of Volterra Integral Equations
• Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind
• Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
• The Order of Numerical Methods for Ordinary Differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Almost-periodic behavior of solutions of a nonlinear Volterra system.
• A Simplex Method for Function Minimization

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