GET_pdf delibra

Volume 8 (2) 2002, 13-26

COMPUTATIONAL METHODS FOR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

Hącia Lechosław

Institute of Mathematics, Poznań University of Technology
Piotrowo 3A, 60-965 Poznań, Poland, e-mail: lhacia@math.put.poznan.pl

DOI:   10.12921/cmst.2002.08.02.13-26

OAI:   oai:lib.psnc.pl:532

Abstract:

Integral equations in space-time play very important role in mechanics and technology. Particular cases of these equations called mixed integral equations or Volterra-Fredholm integral equations arise in the heat conduction theory [4, 6] and the diffusion theory. Moreover, a current density in electromagnetism is determined by the Volterra-Fredholm integral equations [4]. Nonlinear counterparts of the equations studied in [1] are mathematical models of the spatio-temporal development of an epidemic (the spread of the disease in the given population). Some initial-boundary problems for a number of partial differential equations in physics are reducible to the considered integral equations [2- 3, 6], In this paper the general theory of these equations is used in the projection methods. Presented methods lead to a system of algebraic equations or to a system of Volterra integral equations. The convergence of studied algorithm is proved, the error estimate is established. The presented theory is illustrated by numerical examples.

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