online read us now
Paper details
Number 2 - June 2000
Volume 10 - 2000
Solving parabolic equations by using the method of fast convergent iterations
Victor Bondarenko, Peter Bidyuk, Julia Bernatska
Abstract
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.
Keywords
parabolic equations, fundamental solution, Riemannian manifold, rate of convergence, iteration technique, numerical simulation