PathFinderQuad.m

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PathFinderQuad.m#

One of the two main functions. This function takes information about the oscillatory integral

\[ I = \int_\gamma f(z)\mathrm{e}^{\mathrm{i}\omega g(z)}\mathrm{d} z \]

and returns weights \(w_j\) and nodes \(z_j\) such that

\[ I \approx \sum_{j=1}^N f(z_j)w_j \]
[z,w] = PathFinderQuad(a, b, phaseIn, freq, nPts, varargin)

Inputs#

  • a and b are the endpoints of the integration contour \(\gamma\).

  • phaseIn : Coefficients of the polynomial phase function \(g\).

  • freq : The frequency parameter \(\omega\).

  • nPts : The number of quadrature points per contour.

  • varargin : This function takes many optional inputs, which can modify approximation parameters, and request plots. For more information, see Usage.

Outputs#

  • z : Nodes \(z_j\).

  • w : Weights \(w_j\).

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