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Jitse Niesen — Software

Exponential integrators

Linear algebra

    Eigen logo
  • I made several contributions to Eigen; in particular, I contributed the MatrixFunctions module. Eigen is a C++ template library for linear algebra: vectors, matrices, and related algorithms. It aims to be versatile, fast, elegant and compiler-friendly. The MatrixFunctions module contains a general routine for the computations of analytic matrix functions, with specializations for the sine, cosine, hyperbolic sine, and hyperbolic cosine. The module also implements specific algorithms for the matrix exponential, logarithm and square root. All algorithms are taken from the literature.

Evans functions

  • MagnusEvans.nb : Mathematica notebook file for evaluating the Evans function using Magnus integration. Written by Simon Malham, email simonm [at] ma.hw.ac.uk for details.
  • evans_matlab.tar.gz : collection of Matlab scripts for evaluating the Evans function. This archive includes the Fisher problem, the autocatalysis problem (for various parameter values) and the Gray-Scott problem. Methods included are the fourth-order Magnus and Gauss-Legendre and the classical Runge-Kutta method. Type "help evans" to get an overview of the possibilities.
  • scalar_fig.m : Matlab script for reproducing the plots in the paper "Evaluating the Evans function: Order reduction in numerical methods" by Simon Malham and Jitse Niesen.

Symmetries of differential equations