Geodesic
Solving Parabolic Equations by Using the Method of Fast Convergent Iterations
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 333-344.

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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: fundamental solution, Riemannian manifold, rate of convergence, iteration technique, numerical simulation, parabolic equations
Mots-clés : równanie paraboliczne, rozwiązanie podstawowe, symulacja numeryczna 
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     author = {Bondarenko, V. and Bidyuk, P. and Bernatska, J.},
     title = {Solving {Parabolic} {Equations} by {Using} the {Method} of {Fast} {Convergent} {Iterations}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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Bondarenko, V.; Bidyuk, P.; Bernatska, J. Solving Parabolic Equations by Using the Method of Fast Convergent Iterations. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 333-344. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_2_a7/