Bondarenko, Victor ; Bidyuk, Petro ; Bernatska, Julia
Korbicz, Józef - red. ; Uciński, Dariusz - red.
Solving parabolic equations by using the method of fast convergent iterations
Group publication title:
Subject and Keywords:
parabolic equations ; fundamental solution ; Riemannian manifold ; rate of convergence ; iteration technique ; numerical simulation
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.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 10, number 2 (2000) ; click here to follow the link