1D MLSM and FDM comparison
From Medusa: Coordinate Free Meshless Method implementation
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Different numerical approaches to solving a 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>
were analysed. Theoretically, FDM and MLSM should match completely. This is practivaly demonstrated up to certain discretization level.
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