Numerical Solution of a parabolic system with blowup of the solution
This work addresses the numerical treatment of blowup phenomena in nonlinear heat conduction systems, but the results are limited to particular parameter values and the method is incremental.
The paper proposes a numerical method for a parabolic system with blowup solutions, proves that the numerical solution also blows up in finite time, and obtains an estimate of the blowup time with convergence for specific parameter values.
In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular values of the parameters.