Implicit Runge-Kutta methods for singularly perturbed integro-differential systems

DOI10.1016/0168-9274(95)00053-WzbMath0840.65140OpenAlexW2087297463MaRDI QIDQ1902075

Jean-Paul Kauthen

Publication date: 7 July 1996

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

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00053-w

zbMATH Keywords

convergencenumerical exampleimplicit Runge-Kutta methodsextended Pouzet-Volterra-Runge-Kutta methodssystems of singularly perturbed Volterra integro-differential equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Systems of nonlinear integral equations (45G15)

Related Items

A posteriori error estimation in maximum norm for a system of singularly perturbed Volterra integro-differential equations ⋮ Piecewise-quasilinearization techniques for singularly perturbed Volterra integro-differential equations ⋮ Uniform difference method for singularly perturbed Volterra integro-differential equations ⋮ Implicit Runge-Kutta methods for singularly perturbed integro-differential systems ⋮ A survey of singularly perturbed Volterra equations ⋮ Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations ⋮ A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer ⋮ Unnamed Item ⋮ A novel parameter-uniform numerical method for a singularly perturbed Volterra integro-differential equation ⋮ Numerical Analysis and Computational Solution of Integro-Differential Equations ⋮ Regularizing properties of difference schemes for singular integral-differential equations ⋮ Unnamed Item ⋮ Rigorous results on the asymptotic solutions of singularly perturbed nonlinear Volterra integral equations ⋮ Difference schemes of exponential type for singularly perturbed Volterra integro-differential problems ⋮ A posteriori error estimation for a singularly perturbed Volterra integro-differential equation ⋮ Numerical solution of a singularly perturbed Volterra integro-differential equation ⋮ A perspective on the numerical treatment of Volterra equations ⋮ Richardson Extrapolation Method on an Adaptive Grid for Singularly Perturbed Volterra Integro-Differential Equations ⋮ Implicit Runge-Kutta methods for some integrodifferential-algebraic equations ⋮ Tension spline collocation methods for singularly perturbed Volterra integro-differential and Volterra integral equations ⋮ A uniformly convergent numerical method for a singularly perturbed Volterra integro-differential equation

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular perturbation analysis of an integrodifferential equation modelling filament stretching
• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• The numerical treatment of Volterra integro-differential equations with unbounded delay
• Implicit Runge-Kutta methods for some integrodifferential-algebraic equations
• Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
• Implicit Runge-Kutta methods for singularly perturbed integro-differential systems
• Singularly Perturbed Volterra Integral Equations II
• A nonlinear singularly perturbed Volterra integrodifferential equation of nonconvolution type
• A nonlinear singularly perturbed Volterra integrodifferential equation occurring in polymer rheology
• Singularly Perturbed Volterra Integral Equations
• A Nonlinear Volterra Integrodifferential Equation Describing the Stretching of Polymeric Liquids