臺灣博碩士論文加值系統

考慮一個對流擴散方程u_t=u_{xx}+\alpha(u^m)_x+u^{\beta}, (0< x< 1,~ 0<t)，其中 beta>m>=1 去探討它的數值爆炸問題以及解的收斂性

We consider a finite difference scheme for the convective reaction-diffusion equation $u_t=u_{xx}+\alpha(u^m)_x+u^{\beta}, (0< x< 1,~ 0<t)$, where $\beta>m\geqslant 1$ and $\alpha>0$ are parameters. For many differential equations or systems the solutions can become unbounded in finite time $T$. Here the phenomena that is known as blow-up and the finite time $T$ is called the blow-up time. In this paper, we prove that the numerical blow-up time converges to the blow-up time with uniform temporal grid size.

Introduction
Local Convergence
Convergence of the Numerical Blow-up Time
Conclusion

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