Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. Part II. Indirect approximation


In this paper, we continue the study initiated in our previous work [3] 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 [3] 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 [2], where the problem is solved in a Hamiltonian setting. At the same time we improve our previous results reported in [4]


C. I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis,
D. Trif
Babes-Bolyai University, Faculty of Mathematics and Computer Science


Nonlinear reaction-diffusion, positive solution, conserved integral,
projection-like method, f.e.m., finite elements–finite differences method, nonlinear stability, energetic method.

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C.I. Gheorghiu, D. Trif, Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem.
Part II. Indirect approximation, Rev. Anal. Numér. Théor. Approx. 31 (2002) 163-170.


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Rev. Anal. Numer. Theor. Approx.

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Editura Academiei Romane

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[8] Stuart, A. M. and Humphries, A. R., Dynamical systems and numerical analysis, Cambridge Monographs on Applied and Computational Mathematics, Cambridge Univ. Press., 1996

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