1 research outputs found
Efficient approximation of the solution of certain nonlinear reaction--diffusion equation II: the case of large absorption
We study the positive stationary solutions of a standard finite-difference
discretization of the semilinear heat equation with nonlinear Neumann boundary
conditions. We prove 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
-approximation of such a solution by means of a homotopy continuation
method. The cost of our algorithm is {\em linear} in the number of nodes
involved in the discretization and the logarithm of the number of digits of
approximation required