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2.2.7 Parabolic PDE: example

Figure 3: Euler scheme for heat equation.
\includegraphics[width=8cm]{images/pde1d_solve_heat_spikes_simple_i200n500dt01.ps} \includegraphics[width=8cm]{images/pde1d_solve_heat_spikes_simple_i200n100dt05.ps}
Examples for ``spikes'' initial condition (red) and periodic boundaries are displayed in Fig. 3 for two time-steps \bgroup\color{DEFcolor}$\Delta tK/\Delta x^2$\egroup=0.1, 0.5 after 500 or 100 steps, respectively (blue).

The slightly too large time-step (0.5) causes the non-decaying spurious oscillations in the right panel.

The simple discretization (85) gives reasonable results.