TY - JOUR
AU - Gheorghiu, Călin-Ioan
AU - Trif, Damian
PY - 2002/02/01
Y2 - 2024/06/14
TI - Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. I. Direct (variational)
JF - Rev. Anal. Numér. Théor. Approx.
JA - Rev. Anal. Numér. Théor. Approx.
VL - 31
IS - 1
SE - Articles
DO - 10.33993/jnaat311-709
UR - https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art8
SP - 61-69
AB - <pre>We consider a nonlinear, second-order, two-point boundary value </pre><pre>problem that models some reaction-diffusion precesses. When the </pre><pre>reaction term has a particular form, \(<span>f(u)=u^{3}\)</span>, the problem has </pre><pre>a unique positive solution that satisfies a conser<span>ved</span> integral </pre><pre>condition. We study the bifurcation of this solution with respect </pre><pre>to the length of the interval and it turns out that solution </pre><pre>bifurcates from infinity. In the first part, we obtain the </pre><pre>numerical approximation to the positive solution by </pre><pre><em>direct variational</em> methods, while in the second part we consider <em>indirect </em>numerical methods. In order to obtain <em>directly</em> accurate numerical approximations to this positive solution, we </pre><pre>characterize it by a variational problem involving a conditional </pre><pre>extremum. Then we carry out some numerical experiments by usual </pre><pre>finite elements method.</pre>
ER -