## 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 [4]

## Authors

C. I.

Tiberiu Popoviciu Institute of Numerical Analysis,

**Gheorghiu**Tiberiu Popoviciu Institute of Numerical Analysis,

D.

Babes-Bolyai University, Faculty of Mathematics and Computer Science

**Trif**Babes-Bolyai University, Faculty of Mathematics and Computer Science

## Keywords

Nonlinear reaction-diffusion, positive solution, conserved integral,

projection-like method, f.e.m., finite elements–finite differences method, nonlinear stability, energetic method.

## Paper coordinates

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.

## About this paper

##### Journal

Rev. Anal. Numer. Theor. Approx.

##### Publisher Name

Editura Academiei Romane

##### Paper on journal website

##### Print ISSN

1222-9024

##### Online ISSN

2457-8126

##### MR

?

##### ZBL

?

##### Google Scholar Profile

google scholar link

Section 1

Section 2

Section 1

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*On the significance of integral properties of orbits in some superlinear fixed-period problems*, Proc. ICNODEA, Cluj-Napoca, 2001.[3] Gheorghiu, C. I. and Trif, D.,

*Direct and indirect approximations to positive solutions for a nonlinear reaction-diffusion problem*, I. Direct (variational) approximation, this journal, 31 no. 1, pp. 61–70, 2002.[4] Gheorghiu, C. I. and Trif, D.,

*The numerical approximation to positive solution for some reaction-diffusion problems*, Pu.M.A., 11 , pp. 243–253, 2001.[5] Henry, D.,

*Geometric theory of semilinear parabolic equations*, Lecture Notes in Mathematics, 840, Springer-Verlag, 1981.[6] Iserles, A.,

*A First Course in the Numerical Analysis of Differential Equations*, Cambridge Univ. Press, 1996.[7] Larsson, S. and Sanz-Serna, J. M.,

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*Dynamical systems and numerical analysis*, Cambridge Monographs on Applied and Computational Mathematics, Cambridge Univ. Press., 1996