Runge-Kutta time discretizations of parabolic Volterra integro- differential equations

DOI10.1216/jiea/1181075847zbMath0832.65141OpenAlexW2088142981MaRDI QIDQ1900686

Hermann Brunner, Alexander Ostermann, Jean-Paul Kauthen

Publication date: 11 March 1996

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181075847

zbMATH Keywords

numerical experimentsimplicit Runge-Kutta methodsoptimal convergenceabstract Volterra integro-differential equationsparabolic Volterra integro-partial differential equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (max. 100)

Implicit Runge-Kutta methods for singularly perturbed integro-differential systems ⋮ Numerical Analysis and Computational Solution of Integro-Differential Equations ⋮ Numerical solutions of viscoelastic bending wave equations with two term time kernels by Runge-Kutta convolution quadrature ⋮ Unnamed Item ⋮ Numerical solution of evolutionary integral equations with completely monotonic kernel by Runge–Kutta convolution quadrature ⋮ Semi-discrete finite element approximations for linear parabolic integro-differential equations with integrable kernels ⋮ Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations.

Uses Software

• RODAS

Cites Work

• Geometric theory of semilinear parabolic equations
• The method of lines for parabolic partial integro-differential equations
• Numerical methods for hyperbolic and parabolic integro-differential equations
• Time Discretization of an Integro-Differential Equation of Parabolic Type
• Finite element methods for parabolic and hyperbolic partial integro-differential equations
• Resolvent Operators for Integral Equations in a Banach Space
• Finite Difference Approximations for a Class of Semilinear Volterra Evolution Problems
• Evolutionary Integral Equations and Applications
• Runge-Kutta Methods for Parabolic Equations and Convolution Quadrature
• On Fully Discrete Galerkin Approximations for Partial Integro-Differential Equations of Parabolic Type
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