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Iterative-Collocation Method for Integral Equations of Heat Conduction Problems

  • Lechosław Ha̧cia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)

Abstract

The integral equations studied here play very important role in the theory of parabolic initial-boundary value problems (heat conduction problems) and in various physical, technological and biological problems (epidemiology problems). This paper is concerned with the iterative-collocation method for solving these equations. We propose an iterative method with corrections based on the interpolation polynomial of spatial variable of the Lagrange type with given collocation points. The coefficients of these corrections can be determined by a system of Volterra integral equations. The convergence of the presented algorithm is proved and an error estimate is established. The presented theory is illustrated by numerical examples and a comparison is made with other methods.

AMS Subject Classification: 65R20.

Keywords

integral equations in space-time iterative-collocation method interpolating polynomial  correction function 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Lechosław Ha̧cia
    • 1
  1. 1.Institute of Mathematics, Faculty of Electrical Engineering, Poznan University of Technology, Piotrowo 3a, 60-965 PoznanPoland

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