In this article, a system of parabolic equations with nonlinear boundary conditionsis transformed into a system of self-similar (automodel) equations by applying a shapeshifting. Anasymptotics for a compact supporting solution of the problem is proposed. The obtained asymptoticformulas are used as an initial approximation in the numerical solution of the problem. In numericalexperiments k = 3 is taken, a finite-difference scheme is proposed, and a Python program is developedto perform computations for various parameter values, corresponding graphs obtained.Numerical experiments have shown that the iterative processes converge within 3 to 5 steps. Thecompactly supported self-similar asymptotic solution used as the initial approximation played animportant role in ensuring the convergence of the iterative process. The graphs illustrate that, fordifferent numerical parameter values, the reaction–diffusion processes occur at a finite speed.
| Mualliflar | Rakhmonov, Zafar, Zaripova, Aziza |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 187-198 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2026-2-22 |
DOI: 10.29229/uzmj.2026-2-22 · Maqolaning asl sahifasi
System of nonlinear equations,, reaction-diffusion, global solution, asymptotic, numer- ical solution.
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