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Consider the following PDE: $$ \begin{align} &u_t+uu_x=0.1u_{xx},\qquad 00\\ &u(x+1,t)=u(x,t),\qquad t\geq 0 \\ &u(x,0) = \sin 2\pi x,\qquad 0\leq x\leq 1 \end{align} $$

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: Using Finite Difference Using Spectral Method

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?

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