Difference between revisions of "1D MLSM and FDM comparison"
From Medusa: Coordinate Free Mehless Method implementation
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The interval <math>[0, 1]</math> was always discretized uniformly using $N$ nodes, <math>x_i = a+i h, h = (b-a)/N</math>. | The interval <math>[0, 1]</math> was always discretized uniformly using $N$ nodes, <math>x_i = a+i h, h = (b-a)/N</math>. | ||
| − | == Dirichlet | + | == Dirichlet case == |
Revision as of 11:35, 13 March 2017
Different numerical approaches to solving a Dirichlet or Neumann problem
\(
\begin{align*}
\text{Dirichlet} && \text{Neumann} \\
f''(x) &= 2x^2+5 \text{ on } (0, 1) & f''(x) &= 2x^2+5 \text{ on } (0, 1) \\
f(0) &= 1 & f'(0) &= 1 \\
f(1) &= 1 & f(1) &= 1 \\
f(x) &= \frac{1}{6} \left(x^4+15 x^2-16 x+6\right) & f(x) &= \frac{1}{6} \left(x^4+15 x^2+6 x-16\right)
\end{align*}
\)
were analysed. Theoretically, FDM and MLSM should match completely. This is practivaly demonstrated up to certain discretization level.
The interval \([0, 1]\) was always discretized uniformly using $N$ nodes, \(x_i = a+i h, h = (b-a)/N\).
