Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels

DOI10.1007/s10543-007-0122-3zbMath1120.65135OpenAlexW1997153897MaRDI QIDQ996809

Barbara Zubik-Kowal, Zdzisław Jackiewicz, Frank C. Hoppensteadt

Publication date: 19 July 2007

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-007-0122-3

zbMATH Keywords

numerical examplesRunge-Kutta methodsnonlinear Volterra integral equationsnonlinear Volterra integro-differential equationsvariable stepsize algorithms

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10)

Related Items (17)

The Barycentric Rational Difference-Quadrature Scheme for Systems of Volterra Integro-differential Equations ⋮ Collocation methods for nonlinear convolution Volterra integral equations with multiple proportional delays ⋮ Recent advances in the numerical solution of Volterra integral equations ⋮ An efficient spectral method for solving third-kind Volterra integral equations with non-smooth solutions ⋮ Block boundary value methods for solving Volterra integral and integro-differential equations ⋮ The barycentric rational predictor-corrector schemes for Volterra integral equations ⋮ On the numerical stability of the linear barycentric rational quadrature method for Volterra integral equations ⋮ Parallel computations and numerical simulations for nonlinear systems of Volterra integro-differential equations ⋮ Numerical methods based on the Floater-Hormann interpolants for stiff VIEs ⋮ Unnamed Item ⋮ Implementation of general linear methods for Volterra integral equations ⋮ Equivalent probability density moments determine equivalent epidemics in an SIRS model with temporary immunity ⋮ Numerical Solutions and Their Error Bounds for Oscillatory Neural Networks ⋮ Collocation methods for Volterra integral and integro-differential equations: a review ⋮ A new code for Volterra integral equations based on natural Runge-Kutta methods ⋮ General linear methods with large stability regions for Volterra integral equations ⋮ Unnamed Item

Uses Software

• Matlab
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite
• Algorithm 689

Cites Work

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• Remarks on Picard-Lindelöf iteration
• Time point relaxation methods for Volterra integro-differential equations
• Integral equation models for endemic infectious diseases
• A family of embedded Runge-Kutta formulae
• Runge-Kutta theory for Volterra integrodifferential equations
• A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
• Weakly connected neural networks
• Discrete-time waveform relaxation Volterra-Runge-Kutta methods: Convergence analysis
• Extended explicit Bel'tyukov pairs of orders 4 and 5 for Volterra integral equations of the second kind
• Convergence of Dynamic Iteration Methods for Initial Value Problems
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
• Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind
• Some Extended Explicit Bel'tyukov Pairs for Volterra Integral Equations of the Second Kind
• Runge-Kutta triples
• Numerical Solution of Ordinary Differential Equations

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