This package was originally written to solve systems of integro-differential equations via collocation method in arbitrary number of variables. The current implementation of the method is based on a finite dimensional orthogonal system of functions. Therefore additional modules were required to achieve this goal.
The modules are listed below:
Consists of one class called Measure which performs measure theoretic computations such as:
- calculate the measure of a set according to the given measure;
- calculate the integral of a function w.r.t. the measure;
- calculate the norm-p of a given function;
- generate samples from the support of the measure according to the distribution.
Consists of a class called OrthSystem which produces orthogonal systems of functions according to a basis provided as a priori. It takes a measure on a given set and a finite set of independent functions such as polynomials or Fourier series, and generates an orthonormal basis w.r.t. the measure. Then, given a function, it also computes coefficients of the corresponding series.
The interpolation module consists of Interpolation class. This class provides multi-variate interpolation.
The class Collocation, takes a list of symbolic integro-differential equations, an orthonormal system of functions and some collocation points (if provided) then finds approximate solutions of the system.
The SubRegion class partitions the region into sub-regions, solve the system of Integro-differential equations on each and glue them together.
This module provides basic command to illustrate 2D and 3D plots of symbolic or numeric functions based on matplotlib. The 3D plots also include interactive ones based on mayavi.
For more detals refer to the documentation.
To build the documentation run:
$ sphinx-build -b html ./doc/ ./doc/_build
or from ./doc run $ make html.
To generate a pdf file run $ make latexpdf. This requires latex to be available.