Geodesic
Application of the modified boundary element method for the solution of parabolic problems
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 93-101

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An algorithm for finding numerically-analytical solution of parabolic problems (diffusion and heat conduction) is proposed. The problem is solved by the proposed algorithm in three steps. At the first step the one-dimensional problem is solved for a base interval of integration. This problem is of independent significance as well as the basis for the second step. At the second step the two-dimensional parabolic problem is considered. Its solution is performed using the modified boundary elements method. At the third step, the method of step-by-step integration over time is used.
Keywords: linear parabolic equation, modified boundary element method, numerical-analytical integration. 
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     author = {V. P. Fedotov and O. A. Nefedova},
     title = {Application of the modified boundary element method for the solution of parabolic problems},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {93--101},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_4_a11/}
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V. P. Fedotov; O. A. Nefedova. Application of the modified boundary element method for the solution of parabolic problems. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 93-101. http://geodesic.mathdoc.fr/item/VSGTU_2011_4_a11/