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

Călin Ioan Gheorghiu; Damian Trif

doi:10.33993/jnaat312-720

Authors

Călin Ioan Gheorghiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Damian Trif “Babes-Bolyai” University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat312-720

Keywords:

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

Abstract views: 232

Abstract

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 [3].

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