Solving Volterra integro-differential equations by variable stepsize block BS methods: properties and implementation techniques

DOI10.1016/j.amc.2014.04.030zbMath1334.65207OpenAlexW1966492339MaRDI QIDQ274351

A. M. Nagy, Francesca Mazzia

Publication date: 22 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.04.030

zbMATH Keywords

Volterra integro-differential equationsvariable stepsizeconvergence and stabilityblock BS methodsboundary value methods

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

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Uses Software

• Matlab
• VIDEBS

Cites Work

• Block boundary value methods for solving Volterra integral and integro-differential equations
• Boundary value methods for Volterra integral and integro-differential equations
• Quadrature formulas descending from BS Hermite spline quasi-interpolation
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• The BS class of Hermite spline quasi-interpolants on nonuniform knot distributions
• Runge-Kutta theory for Volterra integrodifferential equations
• Stability properties of some boundary value methods
• Block boundary value methods for linear Hamiltonian systems
• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• A hybrid mesh selection strategy based on conditioning for boundary value ODE problems
• Convergence and stability of boundary value methods for ordinary differential equations
• On the relations between B\(_2\)VMs and Runge-Kutta collocation methods
• Singularly perturbed integral equations
• Convergence and Stability of Multistep Methods Solving Nonlinear Initial Value Problems
• The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods
• Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind
• Block-Boundary Value Methods for the Solution of Ordinary Differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• B‐Spline Linear Multistep Methods and their Continuous Extensions
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