Recent advances in the numerical solution of Volterra integral equations

DOI10.22124/jmm.2020.17997.1554zbMath1499.65735OpenAlexW3113944686MaRDI QIDQ5025109

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Publication date: 1 February 2022

Full work available at URL: https://jmm.guilan.ac.ir/article_4461_522a9497c7ab9968792f8dd1d29f9d37.pdf

zbMATH Keywords

Volterra integral equationsgeneral linear methodsNordsieck techniqueimplementation issuesnatural Volterra Runge-Kutta methods

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20)

Related Items (1)

The barycentric rational predictor-corrector schemes for Volterra integral equations

Uses Software

• DIMSIM

Cites Work

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• Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs
• Two-step diagonally-implicit collocation based methods for Volterra integral equations
• Construction of efficient general linear methods for stiff Volterra integral equations
• An extension of general linear methods
• General linear methods for Volterra integral equations
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• Multistep collocation methods for Volterra integral equations
• Automatic selection of the initial step size for an ODE solver
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• Rational functions for guaranteed and experimentally well-conditioned global interpolation
• Implementation of DIMSIMs for stiff differential systems
• Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability
• An approximation method for solving systems of Volterra integro-differential equations
• Experiments with a variable-order type 1 DIMSIM code
• Implementation of second derivative general linear methods
• Implementation of general linear methods for Volterra integral equations
• A new code for Volterra integral equations based on natural Runge-Kutta methods
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• Construction and implementation of two-step continuous methods for Volterra integral equations
• Natural Volterra Runge-Kutta methods
• Two-step almost collocation methods for Volterra integral equations
• Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations
• On the Stability of Volterra–Runge–Kutta Methods
• Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind
• Variable Step Size Predictor-Corrector Schemes for Second Kind 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
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
• Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind
• Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
• The Barycentric Rational Difference-Quadrature Scheme for Systems of Volterra Integro-differential Equations
• Barycentric Lagrange Interpolation
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• Numerical Methods for Ordinary Differential Equations

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