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

Kouame Beranger Edja, Kidjegbo Augustin Toure and Brou Jean-Claude Koua

Journal of Mathematics Research, 2018, vol. 10, issue 5, 119-128

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.

Keywords: numerical blow-up; heat equation; nonlinear boundary; finite difference; arc length transformation; Aitken method (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:5:p:119

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