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Warianty tytułu
Języki publikacji
Abstrakty
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.
Rocznik
Tom
Strony
13--26
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Institute of Mathematics, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland
Bibliografia
- [1] H. Brunner, SIAM J. Numer. Anal., 27, 987-1000 (1990).
- [2] L. Hącia, Zeit. Ang. Math. Mech., 76, 415-416 (1996).
- [3] L. Hącia, Demon. Math. 32, 795-805 (1999).
- [4] L. Hącia, R. Nawrowski, Computer Applications in Electrical Engineering - Monograph ZKwE,60-78 (2002).
- [5] J. P. Kauthen, Numer. Math., 56, 409-429 (1989).
- [6] A. Piskorek, Integral equations - theory and applications, WNT, Warszawa 1997 (in Polish).
- [7] W. I. Tivončuk, Diff. Uravn., 2(9), 1228-1238 (1966) - in Russian.
- [8] I. N. Tukalevska, II Sc. Conf. of Young Ukr. Math., Naukova Dumka, Kiev 1966, 609-613 - in Ukrainian.
- [9] I. H. Sloan, B. J. Burn, J. Int. Equ., 1, 77-94 (1979).
- [10] I. H. Sloan., J. Int. Equ., 265-274 (1980).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a7559a3c-3c0a-4dfa-a2ab-16dc1c9c51fc