Fully Discrete Adaptive Methods for a Blow-up Problem
نویسنده
چکیده
We present adaptive procedures in space and time for the numerical study of positive solutions to the following problem, ut(x, t) = (u)xx(x, t) (x, t) ∈ (0, 1)× [0, T ), (u)x(0, t) = 0 t ∈ [0, T ), (u)x(1, t) = u(1, t) t ∈ [0, T ), u(x, 0) = u0(x) x ∈ (0, 1), with p,m > 0. We describe how to perform adaptive methods in order to reproduce the exact asymptotic behavior (the blow-up rate and the blow-up set) of the continuous problem.
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