我們考慮對於半線性熱方程和其非負初始質以及Dirichlet邊界條件的有限差分近似. 我們知道,雖然半線性熱方程在有限時間爆炸是可以有方法和使用適當的時間網格去證明,但在數值爆炸集合方面卻不一定會與真實的一致. 而在這篇文章中, 我們的目的是使用不同的時間網格來尋找數值爆炸集合.

We consider the finite difference approximation for the semilinear heat equation
u_t = u_xx+f(u) (0 < t; 0 < x < 1) with nonnegative initial data u(0, x) = u_0(x) (0 < x < 1) and the Dirichlet boundary condition u(t, 0) = u(t, 1) = 0 (t > 0). It is known that although the finite-time blow-up for the semilinear heat equation can be reproduced by a scheme with adaptively-defined time mesh, the numerical blow-up
sets do not always coincide with that of the real one. In this paper, we are aimed to investigate the numerical blow-up sets with respect to different time meshes.

1 Introduction 2
2 Explicit scheme 5
3 Implicit scheme 11
4 Conclusion 15
5 References 16

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