Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind and Their Applications

DOI10.2307/2008652zbMath0658.65137OpenAlexW4247984067MaRDI QIDQ3806768

Rossana Vermiglio, Alfredo Bellen, Zdzisław Jackiewicz, Marino Zennaro

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008652

zbMATH Keywords

Runge-Kutta methodscollocationorder conditionsVolterra integral equations of the second kindnatural continuous extensionscontinuous polynomial spline spaces

Mathematics Subject Classification ID

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

Related Items

Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations ⋮ Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations ⋮ Recent advances in the numerical solution of Volterra integral equations ⋮ The barycentric rational predictor-corrector schemes for Volterra integral equations ⋮ Highly stable Runge-Kutta methods for Volterra integral equations ⋮ Natural Volterra Runge-Kutta methods ⋮ An \textit{hp}-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels ⋮ An efficient numerical algorithm to solve Volterra integral equation of second kind ⋮ Highly stable multistep Runge-Kutta methods for Volterra integral equations ⋮ Continuous Volterra-Runge-Kutta methods for integral equations with pure delay ⋮ General linear methods for Volterra integral equations ⋮ Some applications of continuous Runge-Kutta methods ⋮ On stability of Runge-Kutta methods for delay integral equations ⋮ Global stability analysis of the Runge-Kutta methods for Volterra integral and integro-differential equations with degenerate kernels ⋮ A new code for Volterra integral equations based on natural Runge-Kutta methods ⋮ A perspective on the numerical treatment of Volterra equations

Cites Work

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