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Solving Parabolic Equations by Using the Method of Fast Convergent Iterations

Bondarenko V., Bidyuk P., Bernatska J.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

333-344

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.