Solving Parabolic Equations by Using the Method of Fast Convergent Iterations

• Autorzy: Bondarenko V. , Bidyuk P. , Bernatska J.
• Języki publikacji: EN

Abstrakty

EN

The paper describes an approach to solving parabolic partial differential equations that generalizes the well-known parametrix method. The iteration technique proposed exhibits faster convergence than the classical parametrix approach. A solution is constructed on a manifold with the application of the Laplace-Beltrami operator. A theorem is formulated and proved to provide a basis for finding a unique solution. Simulation results illustrate the superiority of the proposed approach in comparison with the classical parametrix method.

Słowa kluczowe

EN

parabolic equations; fundamental solution; Riemannian manifold; rate of convergence; iteration technique; numerical simulation

PL

równanie paraboliczne; rozwiązanie podstawowe; symulacja numeryczna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2000
• Tom: Vol. 10, no 2
• Strony: 333--344
• Opis fizyczny: Bibliogr. 10 poz., tab., wykr.

Twórcy

autor

Bondarenko V.

autor

Bidyuk P.

autor

Bernatska J.

• Department of Applied Mathematics National Technical University of Ukraine `Kiev Polytechnic Institute' 252056 pr. Peremogy, 37, Kyiv, Ukraine,