Difference between revisions of "1D MLSM and FDM comparison"
From Medusa: Coordinate Free Mehless Method implementation
(Created page with "A sample Dirichlet or Neumann problem <math> \begin{align*} f''(x) &= 2x^2+5 \text{ on } (0, 1)\\ f(0) &= 0 \\ f(1) &= 1 \end{align*} </math>") |
|||
| Line 1: | Line 1: | ||
| − | A sample Dirichlet or Neumann problem | + | A sample Dirichlet or Neumann problem <br> |
<math> | <math> | ||
\begin{align*} | \begin{align*} | ||
| − | 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) &= 0 \\ | + | f(0) &= 1 & f'(0) &= 1 \\ |
| − | f(1) &= 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*} | \end{align*} | ||
</math> | </math> | ||
Revision as of 11:29, 13 March 2017
A sample Dirichlet or Neumann problem
\(
\begin{align*}
f''(x) &= 2x^2+5 \text{ on } (0, 1) & f''(x) &= 2x^2+5 \text{ on } (0, 1) \\
f(0) &= 1 & f'(0) &= 1 \\
f(1) &= 1 & f(1) &= 1 \\
f(x) &= \frac{1}{6} \left(x^4+15 x^2-16 x+6\right) & f(x) &= \frac{1}{6} \left(x^4+15 x^2+6 x-16\right)
\end{align*}
\)
