Consider the following PDE: $ \begin{align} &u_t+uu_x=0.1u_{xx},\qquad 0
I used two different numerical schemes(Finite difference and Spectral method) and implemented it by MATLAB to plot $u$ at $t = 0.21$. The results are very different:
Here are my questions:
- Is there a name for this nonlinear PDE?
- Does the solution to the PDE decay in time?
- [EDITED:]Which one of the figures above is close to the true solution?