scholarly journals Numerical approximation of a parabolic problem with a nonlinear boundary condition

1998 ◽  
Vol 4 (3) ◽  
pp. 497-506 ◽  
Author(s):  
R.G. Duran ◽  
◽  
J.I. Etcheverry ◽  
J.D. Rossi ◽  
Keyword(s):  
Boundary Condition ◽  
Parabolic Problem ◽  
Numerical Approximation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition

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

2019 ◽  
Vol 11 (5) ◽  
pp. 1
Author(s):  
Ardjouma Ganon ◽  
Manin Mathurin Taha ◽  
Kidjégbo Augustin Touré
Keyword(s):  
Boundary Condition ◽  
Numerical Approximation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Mesh Size ◽  
Semilinear Parabolic Equation ◽  
Flux Boundary Condition ◽  
Finite Time Convergence ◽  
Semilinear Parabolic

This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx− λup, 0 < x < 1, t > 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.

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