Journal ArticleDOI
Implicit Runge-Kutta methods for singularly perturbed integro-differential systems
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TLDR
In this article, the convergence of extended implicit Pouzet-Volterra-Runge-Kutta methods applied to singularly perturbed systems of Volterra integro-differential equations and to the associated integrodifferential-algebraic systems is analyzed.About:
This article is published in Applied Numerical Mathematics.The article was published on 1995-09-01. It has received 20 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Runge–Kutta methods.read more
Citations
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Journal ArticleDOI
A perspective on the numerical treatment of Volterra equations
TL;DR: In this paper, the properties and numerical treatment of various types of Volterra and Abel-Volterra integral and integro-differential equations are discussed and discussed in detail.
Journal ArticleDOI
A survey of singularly perturbed Volterra equations
TL;DR: A survey of the existing literature on singularly perturbed Volterra integral and integro-differential equations is given in this article, where convergence results for linear multistep methods applied to singular, possibly weakly singular VOLTERRA integral equations and numerical illustrations are provided.
Journal ArticleDOI
Uniform difference method for singularly perturbed Volterra integro-differential equations
TL;DR: Singularly perturbed Volterra integro-differential equations are considered and an exponentially fitted difference scheme is constructed which gives first order uniform convergence in the discrete maximum norm.
Journal ArticleDOI
Numerical solution of a singularly perturbed Volterra integro-differential equation
TL;DR: In this article, the convergence properties of a difference scheme for singularly perturbed Volterra integro-differential equations on a graded mesh were studied, and it was shown that the scheme is first-order convergent in the discrete maximum norm, independently of the perturbation parameter.
Journal ArticleDOI
Tension spline collocation methods for singularly perturbed Volterra integro-differential and Volterra integral equations
Vilmos Horvat,Mladen Rogina +1 more
TL;DR: In this paper, the authors considered the numerical discretization of singularly perturbed Volterra integro-differential equations (VIDE) and VIE by tension spline collocation methods.
References
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Book
Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.
Book
Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations
K. Dekker,J. G. Verwer +1 more
Journal ArticleDOI
The Numerical Solution of Volterra Equations.
Book
The numerical solution of Volterra equations
TL;DR: In this article, the authors introduce the theory of Volterra Equations, and present a number of methods for computing them, e.g., Runge-Kutta-type methods for VOLTERRA Equations with Regular Kernels.
Journal ArticleDOI
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
TL;DR: A study of Runge-Kutta methods when applied to stiff differential equations containing a small stiffness parameter ε yields sharp error bounds for the stiff problem.
Related Papers (5)
Tension spline collocation methods for singularly perturbed Volterra integro-differential and Volterra integral equations
Vilmos Horvat,Mladen Rogina +1 more