Fredholm-Volterra integral equation with singular kernel.
type: Item
instance of: scholarly article
title: Fredholm-Volterra integral equation with singular kernel.
zbMATH Open document ID: 1034.45004
DOI: 10.1016/S0096-3003(02)00046-2
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: The author considers the Fredholm-Volterra integral equation of the second kind \[ \delta\phi(x,t)+\int\limits_{-1}^1 \left| \ln| y-x| -d\right| \phi(y,t)\,dy+\int\limits_0^t F(\tau)\phi(x,\tau) \,d\tau=f(x,t),\tag{1} \] where \(| x| \leq1,\) \( t\in[0,T],\) \(\lambda\in(0,\infty),\) \(\delta\in(0,\infty]\), with a specific right-hand side \(f(x,t)\), under the condition \[ \int\limits_{-1}^1 \phi(y,t)\,dy=P(t),\qquad \int\limits_{-1}^1y\phi(y,t)\,dy=M(t). \] The equation (1) arises in a contact problem in elasticity. Using the quadrature formula for the second integral, a system of integral equations is obtained with respect to the unknowns \(\phi_k(x)=\phi(x,t_k)\), \(k=1,\ldots,N\). Using the Legendre polynomials the obtained system with the logarithmic kernel is further reduced to an infinite algebraic system. The case \(\delta=0\) (a first kind equation) is considered separately. In conclusion a numerical result is demonstrated.
reviewed by: Roland Duduchava
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 74M15
zbMATH DE Number: 1977955
zbMATH Keywords: Fredholm-Volterra integral equation
zbMATH Keywords: contact problem
zbMATH Keywords: logarithmic kernel
zbMATH Keywords: numerical result
author: M. A. Abdou
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00046-2
OpenAlex ID: W2088711579
description: scientific article; zbMATH DE number 1977955