Quenching for discretizations of a semilinear parabolic equation with nonlinear boundary outflux

Authors

  • Kouakou Cyrille N'Dri Institut National Polytechnique Félix Houphouët-Boigny, Côte d'Ivoire https://orcid.org/0000-0001-6421-8672
  • Ardjouma Ganon Institut National Polytechnique Félix Houphouët-Boigny, Côte d'Ivoire
  • Gozo Yoro Département Mathématiques et Informatique, Université Nangui Abrogoua d'Abobo Adjamé, Abidjan, Côte d'Ivoire
  • Kidjegbo Augustin Touré Institut National Polytechnique Félix Houphouët-Boigny, Côte d'Ivoire

DOI:

https://doi.org/10.33993/jnaat522-1325

Keywords:

Nonlinear parabolic equations, Nonlinear boundary outflux, Semidiscretizations, Numerical quenching, Quenching rate
Abstract views: 130

Abstract

In this paper, we study numerical approximations of a semilinear parabolic problem in one-dimension, of which the nonlinearity appears both in source term and in Neumann boundary condition. By a semidiscretization using finite difference method, we obtain a system of ordinary differential equations which is an approximation of the original problem. We obtain some conditions under which the positive solution of our system quenches in a finite time and estimate its semidiscrete quenching time. Convergence of the numerical quenching time to the theoretical one is established. Next, we show that the quenching rate of the numerical scheme is different from the continuous one. Finally, we give some numerical results to illustrate our analysis.

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References

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Published

2023-12-28

How to Cite

N’Dri, K. C., Ganon, A., Yoro, G., & Touré, K. A. . (2023). Quenching for discretizations of a semilinear parabolic equation with nonlinear boundary outflux. J. Numer. Anal. Approx. Theory, 52(2), 241–252. https://doi.org/10.33993/jnaat522-1325

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