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.
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Ha̧cia, L. (2007). Iterative-Collocation Method for Integral Equations of Heat Conduction Problems. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_45
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DOI: https://doi.org/10.1007/978-3-540-70942-8_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
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