- Equation-free Toolbox for Matlab/Octave
- Download the toolbox via Github This 'equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to use microscopic simulators to perform system level tasks and analysis, because microscale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing only short bursts of of the microscale simulator, and often only computing on small patches of the spatial domain. This suite of functions empowers users to start implementing such methods in their own applications.
- LaTeX style file for Reduce computer algebra
- From late 2011, the computer algebra package Reduce could input a LaTeX document with Reduce code intermingled and Reduce would only execute the code in the environment \begin{reduce}...\end{reduce}. Use the reduce command in_tex "filename"$. Download a LaTeX style file and an example document.
- LaTeX style file to track references to labels
- At every \label, prints pages at which the label is referenced via \ref, \eqref, \autoref, or \cref. One option "disable" which omits the package, but defines the commands that might still be in auxiliary files Download the LaTeX style file: beta version.
- LaTeX style file for section contents in a book/report
- Defines \secttoc for sections in a book. \secttoc then lists contents of a section, one depth deeper than minitoc does for chapters. Download the LaTeX style file.
- Stochastic Differential Equation solver
- Supplies some stochastic differential equation (SDE) solvers for matlab, octave and scilab. An example of their use is also supplied, showing the use for single and multiple independent noise sources. Kloeden and Platen (1992) comprehensively introduced the numerical solution of SDEs. Download the file sde.dtx, then execute LaTeX on sde.dtx to unpack the files.
- Differential Algebraic Equation solver
- Supplies some simple differential algebraic equation (DAE) solvers for matlab, octave and scilab. An example of their use for a pendulum is also supplied. Download the file dae.dtx, then execute LaTeX on dae.dtx to unpack the files.
- Estimate Generalised Fractal Dimensions
- The function fdim() estimates generalised fractal dimensions of a set of given points. This code is based upon traditional methods and is arguably one of the most accurate in its class, and is reasonably computationally efficient. Download and unzip fdimV0.2.zip, then execute Matlab/Octave on eg.m for an example.
- Construct Deterministic/Stochastic Centre/Slow/Invariant Manifolds
-
My repository
WebServicesGit provides source code for using computer
algebra Reduce to construct emergent models of complex
dynamical systems.
- Centre Manifold:
- obtain a centre manifold of your specified system of ordinary differential equations (ODE) or delay differential equations (DDE), when the ODE/DDE has fast and centre modes. This code underlies the web service at http://www.maths.adelaide.edu.au/anthony.roberts/gencm.php
- Stochastic Normal Form:
- derive a stochastic/non-autonomous coordinate transformation that separates slow, stable and unstable modes in a system of SDEs or non-autonomous ODEs (or autonomous ODEs). This coordinate transform immediately gives the reduced model on the stochastic/non-autonomous slow manifold (and also other invariant manifolds), and the corresponding stochastic/non-autonomous isochrons which are so useful for projecting initial conditions and uncertainty quantification. This code underlies the web service at http://www.maths.adelaide.edu.au/anthony.roberts/sdenf.php
- Estimate radius of convergence of a Taylor series
- This Matlab/Octave function estimates the radius of convergence of a Taylor series from its coefficients. The function caters for both cases of when convergence is limited by a single singularity or by a complex conjugate pair of singularities. Also estimates the location and nature of the singularities. Download radiusConverge.m See the Appendix of doi:10.1137/0150091
- Construct an infinite-D coord transform for Burgers-like PDE:
- This Reduce code supports an example in the article Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions Download pBurgers.txt
If you like this web page, please link to it so others can find it more easily.