Collocation Method

This method is named collocation method because it employs two sets of basis functions.

To be specific, the result function should be

\[\psi = \psi(x_0) + \sum_i U_i H_i(x) + \sum_i U'_i S_i(x),\]

where \(\psi(x_0)\) takes care of the boundary condition at \(x_0\).

With two set of basis functions the matrix form of the equation is double sized.

References and Notes

  1. Freitag, K. J. (2007). Neural networks and differential equations.

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