Blow-up for Semidiscretization of Semilinear Parabolic Equation With Nonlinear Boundary Condition

Ardjouma Ganon, Manin Mathurin Taha and Kidjégbo Augustin Touré

Journal of Mathematics Research, 2019, vol. 11, issue 5, 1-10

Abstract: This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx− λup, 0 0, and a nonlinear flux boundary condition ux(0,t) = 0, ux(1,t) = uq(1,t), t > 0. We give conditions under which the positive semidiscrete solution blows up in a finite time. Convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero is established. Finally, we use an efficient algorithm to estimate the blow-up time.

Keywords: semilinear equation; numerical blow-up; nonlinear boundary; finite differences; arc length transformation; Aitken △^2 method (search for similar items in EconPapers)
Date: 2019
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