Two-step diagonally-implicit collocation based methods for Volterra integral equations

DOI10.1016/j.apnum.2012.06.007zbMath1251.65172OpenAlexW1993340003MaRDI QIDQ450891

Dajana Conte, Raffaele D'Ambrosio, Beatrice Paternoster

Publication date: 26 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.007

zbMATH Keywords

stabilityconvergencenumerical examplesnonlinear Volterra integral equationstwo-step Runge-Kutta methodsdiagonally-implicit methodstwo-step collocation methods

Mathematics Subject Classification ID

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

Related Items (20)

Construction and implementation of two-step continuous methods for Volterra integral equations ⋮ A class of two-step collocation methods for Volterra integro-differential equations ⋮ On the stability of \(\vartheta\)-methods for stochastic Volterra integral equations ⋮ Two-step collocation methods for fractional differential equations ⋮ Recent advances in the numerical solution of Volterra integral equations ⋮ The barycentric rational predictor-corrector schemes for Volterra integral equations ⋮ Non-stationary wave relaxation methods for general linear systems of Volterra equations: convergence and parallel GPU implementation ⋮ Optimal Schwarz waveform relaxation for fractional diffusion-wave equations ⋮ Multistep collocation methods for Volterra integro-differential equations ⋮ Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection ⋮ Two-step modified collocation methods with structured coefficient matrices ⋮ Implementation of general linear methods for Volterra integral equations ⋮ Natural Volterra Runge-Kutta methods ⋮ Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution ⋮ Multistep collocation approximations to solutions of first-kind Volterra integral equations ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ GPU-acceleration of waveform relaxation methods for large differential systems ⋮ Collocation methods for Volterra integral and integro-differential equations: a review ⋮ Stability issues for selected stochastic evolutionary problems: a review ⋮ An iterative multistep kernel based method for nonlinear Volterra integral and integro-differential equations of fractional order

Uses Software

• RODAS

Cites Work

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• Two-step modified collocation methods with structured coefficient matrices
• Search for highly stable two-step Runge-Kutta methods
• Construction and implementation of highly stable two-step continuous methods for stiff differential systems
• Two-step almost collocation methods for ordinary differential equations
• Continuous two-step Runge-Kutta methods for ordinary differential equations
• Fast Runge-Kutta methods for nonlinear convolution systems of Volterra integral equations
• Multistep collocation methods for Volterra integral equations
• Fast collocation methods for Volterra integral equations of convolution type
• Two-step almost collocation methods for Volterra integral equations
• Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind
• The Order of Numerical Methods for Ordinary Differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Fast and Oblivious Convolution Quadrature
• A Family of Multistep Collocation Methods for Volterra Integral Equations

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