1D MLSM and FDM comparison: Difference between revisions
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<math> | <math> | ||
\begin{align*} | \begin{align*} | ||
\text{Dirichlet} & \text{Neumann} \\ | \text{Dirichlet} && \text{Neumann} \\ | ||
f''(x) &= 2x^2+5 \text{ on } (0, 1) & f''(x) &= 2x^2+5 \text{ on } (0, 1) \\ | f''(x) &= 2x^2+5 \text{ on } (0, 1) & f''(x) &= 2x^2+5 \text{ on } (0, 1) \\ | ||
f(0) &= 1 & f'(0) &= 1 \\ | f(0) &= 1 & f'(0) &= 1 \\ | ||
Revision as of 09:30, 13 March 2017
A sample Dirichlet or Neumann problem
<math>
\begin{align*}
\text{Dirichlet} && \text{Neumann} \\
f(x) &= 2x^2+5 \text{ on } (0, 1) & f(x) &= 2x^2+5 \text{ on } (0, 1) \\
f(0) &= 1 & f'(0) &= 1 \\
f(1) &= 1 & f(1) &= 1 \\
f(x) &= \frac{1}{6} \left(x^4+15 x^2-16 x+6\right) & f(x) &= \frac{1}{6} \left(x^4+15 x^2+6 x-16\right)
\end{align*} </math>