Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation
Keywords:nonlinear reaction-diffusion, positive solution, conserved integral, projection-like method, f.e.m., finite elements-finite differences method, nonlinear stability, energetic method
AbstractIn this paper we continue the study initiated in our previous work  and design a projection-like algorithm to approximate a hyperbolic unstable "point''. This "point'' is in fact the positive solution of the reaction-diffusion problem considered in  and the algorithm modifies a finite difference (Euler)-finite elements scheme by incorporating the independence of the length of the domain condition. The numerical results are in good agreement with those obtained by direct methods as well as with those reported in , where the problem is solved in a Hamiltonian setting. At the same time we improve our previous results reported in .
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