A numerical simulation for the blow-up of semi-linear diffusion equations

Authors:
F. De La Hoz;F. Vadillo
Affiliations:
Departmento de Matematica Aplicada, Estadi stica e Investigacion Operativa, Universidad del Pai s Vasco-Euskal Herriko Unibertsitatea, Spain;Departmento de Matematica Aplicada, Estadi stica e Investigacion Operativa, Universidad del Pai s Vasco-Euskal Herriko Unibertsitatea, Spain
Venue:
International Journal of Computer Mathematics
Year:
2009

Citing 7
Cited 0

The role of critical exponents in blowup theorems

SIAM Review
A new class of time discretization schemes for the solution of nonlinear PDEs

Journal of Computational Physics
Spectral methods in MatLab

Spectral methods in MatLab
A quasi-steady state solver for the stiff ordinary differential equations of reaction kinetics

Journal of Computational Physics
A MATLAB differentiation matrix suite

ACM Transactions on Mathematical Software (TOMS)
Exponential time differencing for stiff systems

Journal of Computational Physics
Fourth-Order Time-Stepping for Stiff PDEs

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Many mathematical models have the property of developing singularities at a finite time; in particular, the solution u(x, t) of the semi-linear parabolic Equation (1) may blow up at a finite time T. In this paper, we consider the numerical solution with blow-up. We discretize the space variables with a spectral method and the discrete method used to advance in time is an exponential time differencing scheme. This numerical simulation confirms the theoretical results of Herrero and Velzquez [M.A. Herrero and J.J.L. Velzquez, Blow-up behavior of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincare 10 (1993), pp. 131-189.] in the one-dimensional problem. Later, we use this method as an experimental approach to describe the various possible asymptotic behaviours with two-space variables.