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Numerical Blow-up for A Heat Equation with Nonlinear Boundary Conditions

Author

Listed:
  • Kouame Beranger Edja
  • Kidjegbo Augustin Toure
  • Brou Jean-Claude Koua

Abstract

We study numerical approximations of solutions of a heat equation with nonlinear boundary conditions which produce blow-up of the solutions. By a semidiscretization using a finite difference scheme in the space variable we get a system of ordinary differential equations which is an approximation of the original problem. We obtain sufficient conditions which guarantee the blow-up solution of this system in a finite time. We also show that this blow-up time converges to the theoretical one when the mesh size goes to zero. We present some numerical results to illustrate certain point of our work.

Suggested Citation

  • Kouame Beranger Edja & Kidjegbo Augustin Toure & Brou Jean-Claude Koua, 2018. "Numerical Blow-up for A Heat Equation with Nonlinear Boundary Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(5), pages 119-128, October.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:5:p:119
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    More about this item

    Keywords

    numerical blow-up; heat equation; nonlinear boundary; finite difference; arc length transformation; Aitken method;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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