Computational methods for Volterra - Fredholm integral equations

• Autorzy: Hącia L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

integral equations; Volterra-Fredholm integral equations; heat conduction theory; diffusion theory; electromagnetism; nonlinear counterparts; projection method; epidemic

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2002
• Tom: Vol. 8, nr 2
• Strony: 13--26
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Hącia L.

• 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).