Solving parabolic equations by using the method of fast convergent iterations - Bondarenko, Victor; Bidyuk, Petro; Bernatska, Julia (Zielona Góra: Uniwersytet Zielonogórski)
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