Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with large absorption

• Autores: Ezequiel Dratman
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 238, Nº 1, 2013, págs. 180-202
• Idioma: inglés
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• Resumen

  • We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions.Weprove that, if the absorption is large enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the ��continuous�� equation. Furthermore, we exhibit an algorithm computing an å-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.