Iterative-collocation method for integral equations of heat conduction problems

  • Authors:

  • Lechosław Hacia

  • Affiliations:

  • Institute of Mathematics, Faculty of Electrical Engineering, Poznan University of Technology, Poznan, Poland

  • Venue:
  • NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

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.