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Mesh in time: $$ \begin{equation} 0 = t_0 < t_1 < t_2 < \cdots < t_{N_t-1} < t_{N_t} = T \end{equation} $$
Mesh in space: $$ \begin{equation} 0 = x_0 < x_1 < x_2 < \cdots < x_{N_x-1} < x_{N_x} = L \end{equation} $$
Uniform mesh with constant mesh spacings \( \Delta t \) and \( \Delta x \): $$ \begin{equation} x_i = i\Delta x,\ i=0,\ldots,N_x,\quad t_i = n\Delta t,\ n=0,\ldots,N_t \end{equation} $$
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