Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels

  title={Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels},
  author={Petr N. Vabishchevich},

Figures and Tables from this paper

Numerical Solution of the Cauchy Problem for a Second-Order Integro-Differential Equation

In a finite-dimensional Hilbert space, we consider the Cauchy problem for a second-order integro-differential evolution equation with memory where the integrand is the product of a difference kernel

Nonlinear approximation of functions based on non-negative least squares solver

The proposed approach’s key feature consists in determining the first parameter on each separate iteration of the classical non-negative least squares method for a wide enough class of nonlinear approximations characterized by a set of two required parameters.

Reconstructing the Potential of the Generalized Heat Equation

  • A. Khanfer
  • Materials Science
    Journal of Nonlinear Mathematical Physics
  • 2022
We reconstruct the potential q(x) for the generalized heat equation of the form ut-b(x)uxx-a(x)ux-q(x)u=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}

Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations

In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous



Numerical solution of an evolution equation with a positive-type memory term

  • W. McLeanV. Thomée
  • Mathematics
    The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
  • 1993
Abstract We study the numerical solution of an initial-boundary value problem for a Volterra type integro-differential equation, in which the integral operator is a convolution product of a

A Kernel Compression Scheme for Fractional Differential Equations

A method is proposed to reduce costs while controlling the accuracy of the scheme by splitting the fractional integral of a function f into a local term and a history term, and derives a multipole approximation to the Laplace transform of the kernel.

Numerical Approximation of Partial Differential Equations

This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough

Evolutionary Integral Equations And Applications

This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of

Analytical and numerical methods for Volterra equations

  • P. Linz
  • Mathematics
    SIAM studies in applied and numerical mathematics
  • 1985
Some applications of Volterraequations Linear Volterra equations of the second kind Nonlinear equations of the second kind Equations of the first kind Convolution equations The numerical solution of

Nonlinear Approximation Theory

The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima tion is strongly connected with his name. By

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

For Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson

A generalization of a lemma of bellman and its application to uniqueness problems of differential equations

It was first made use of this lemma in discussions of stability problems of differential equations.' Later ~ it was applied to investigations of uniqueness and dependence of the solutions of

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

This study focuses on 1-step methods and approximate the local part of the fractional integral by integral deferred correction schemes for Volterra equations to enable high order accuracy.

Finite Element Methods for Integrodifferential Equations

Some practical problems and their properties parabolic integrodifferential equations a survey of elliptic finite elements semidiscrete and fully discrete schemes saving of storage the case with