Geodesic
Boundary element method and power series method for one-dimensional non-linear filtration problems
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 2-17

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The paper deals with the analytical and numerical study of the nonlinear filtration (diffusion) equation with degeneration, without initial data, at two different boundary value modes. Particularly, a new approach to the construction of problem solutions based on the boundary element method has been proposed, the application results being compared with the solutions obtain with the application of the power series method. Model examples have been considered.
Keywords: partial differential equations; nonlinear filtration (diffusion) equation; boundary value problem; boundary element method; power series method. 
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     author = {A. L. Kazakov and L. F. Spevak},
     title = {Boundary element method and power series method for one-dimensional non-linear filtration problems},
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A. L. Kazakov; L. F. Spevak. Boundary element method and power series method for one-dimensional non-linear filtration problems. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 2-17. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a0/