A parallel method for the numerical solution of integro-differential equation with positive memory.
type: Item
instance of: scholarly article
title: A parallel method for the numerical solution of integro-differential equation with positive memory.
zbMATH Open document ID: 1042.65109
DOI: 10.1016/S0045-7825(03)00442-0
author: Kiwoon Kwon
author: D. Sheen
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2004-01-23T00:00:00Z
review text: The method of the title apply the Fourier-Laplace transformation in time to obtain a set of complex-valued, elliptic problems parameterized by points on a contour in the complex plane. This leads to several elliptic problems (one for each point) and they can be solved in parallel, essentially without data communications. Then the time domain solution can be obtained by the Fourier-Laplace inversion formula. An error analysis of the method is presented, and the method is illustrated in detail by six numerical examples.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 2031348
zbMATH Keywords: integrodifferential equation
zbMATH Keywords: positive memory
zbMATH Keywords: parallel algorithm
zbMATH Keywords: Fourier-Laplace transformation
zbMATH Keywords: Fourier-Laplace inversion formula
zbMATH Keywords: error analysis
zbMATH Keywords: numerical examples
Wikidata QID: Q115339832
reviewed by: Søren Christiansen
MaRDI profile type: Publication
cites work: Q4254603
cites work: Finite Element Methods for Integrodifferential Equations
cites work: Finite Element Approximation of a Parabolic Integro-Differential Equation with a Weakly Singular Kernel
cites work: On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel. I: Smooth initial data
cites work: Propagation of singularities for integrodifferential equations
cites work: Numerical methods for integrodifferential equations of parabolic and hyperbolic types
cites work: APPROXIMATION OF SCALAR WAVES IN THE SPACE-FREQUENCY DOMAIN
cites work: FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES
cites work: Spline Collocation Methods for a Class of Hyperbolic Partial Integro-Differential Equations
cites work: Exponentially convergent parallel discretization methods for the first order evolution equations
cites work: A general theory of heat conduction with finite wave speeds
cites work: Global Existence and Asymptotic Stability for a Semilinear Hyperbolic Volterra Equation with Large Initial Data
cites work: Absorbing boundary conditions for wave propagation in viscoelastic media
cites work: Frequency domain formulation of linearized Navier-Stokes equations
cites work: A frequency-domain parallel method for the numerical approximation of parabolic problems
cites work: Ritz–Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations
cites work: An inverse problem in the theory of materials with memory
cites work: Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
cites work: Numerical solution of an evolution equation with a positive-type memory term
cites work: An integrodifferential equation for rigid heat conductors with memory
cites work: H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations
cites work: On Linear Volterra Equations of Parabolic Type in Banach Spaces
cites work: Positivity and regularity of hyperbolic Volterra equations in Banach spaces
cites work: Error Estimates with Sharp Constants for a Fading Memory Volterra Problem in Linear Solid Viscoelasticity
cites work: Q4792245
cites work: A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
cites work: A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
cites work: The Accurate Numerical Inversion of Laplace Transforms
cites work: Long-Time Numerical Solution of a Parabolic Equation with Memory
cites work: Error Estimates for Semidiscrete Finite Element Methods for Parabolic Integro-Differential Equations
cites work: Numerical Inversion of Laplace Transforms Using Laguerre Functions
cites work: Orthogonal Spline Collocation Methods for Some Partial Integrodifferential Equations
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description: scientific article; zbMATH DE number 2031348