The approximate solution of initial-value problems for general Volterra integro-differential equations

DOI10.1007/BF02247941zbMath0631.65141OpenAlexW1482982963MaRDI QIDQ1094851

Hermann Brunner

Publication date: 1988

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02247941

zbMATH Keywords

numerical examplesVolterra integro-differential equationsorder of discrete convergencepolynomial spline collocation methodsRunge-Kutta-Nyström type methods

Mathematics Subject Classification ID

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

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Cites Work

• High-order methods for the numerical solution of Volterra integro- differential equations
• Collocation methods for second-order Volterra integro-differential equations
• Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations
• An integro-differential equation with application in heat flow
• A model for one-dimensional, nonlinear viscoelasticity
• Taylor Series Methods for the Solution of Volterra Integral and Integro-Differential Equations
• Volterra integral and differential equations
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