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Systems of Ordinary Differential Equations 13 (RubySode)

Systems of Ordinary Differential Equations 13 (RubySode)


Systems of Ordinary Differential Equations RubySode is a Ruby program to generate a Ruby program to solve ordinary equations. more>>
Systems of Ordinary Differential Equations RubySode (Sode.rb) is a Ruby program to generate a Ruby program to solve a single (or a system of) ordinary differential equation(s). A long Taylor series method, pioneered by Prof. Y.F. Chang, who taught at the University of Nebraska in the late 1970s when I was a graduate student there, is used.
The number of Taylor series terms can be specified in the problem file, though it is usually 30.
Enhancements:
- Minir code cleanup. Some tests have been made more meaningful (add, sub, mult, and div).
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Added: 2007-05-31 License: GPL (GNU General Public License) Price:
877 downloads
 
Other version of Systems of Ordinary Differential Equations
Systems of Ordinary Differential Equations 08Systems of Ordinary Differential Equations uses long Taylor series to solve systems of ordinary
License:GPL (GNU General Public License)
Download (0.033MB)
940 downloads
Added: 2007-03-28
Simple Equation 0.9

Simple Equation 0.9


Simple Equation makes it simple to put equations on the Web. more>>
Simple Equation makes it simple to put equations on the Web. Simple Equation project does not bother the user with the layout of the equation; it just displays it. The focus is on being simple to use.

One of the biggest obstacles to using mathematical expressions on the web is that the user currently needs to worry about layout. Web users should not have to learn a layout engine.

The class is built as a recursive parser. It is pretty easy to add operations to the parser, but it will not scale to a huge set of operations. That is OK, we want to keep things simple. At some point a layout engine may be required for a complexity level. This is not a layout engine.

Currently, only graphical output is generated, but it is hoped that MathML output can be generated automatically if the browser supports it instead of the graphic.

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Added: 2007-04-25 License: Free for non-commercial use Price:
912 downloads
Equation Grapher 20050225

Equation Grapher 20050225


Equation Grapher is a 2D implicit equation grapher. more>>
Equation Grapher is a 2D implicit equation grapher.

Equation Grapher allows you to plot equations of the form f(x,y) = g(x,y), with all of the standard operators (log, exp, sqrt, ...) as well as differentiation.

Example equations:

y = sin(x)
x = sin(y)
(xy)^2 = sin(cos(x^2 + y^2))
y = deriv(exp(-x^2/2),x)

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Download (0.45MB)
Added: 2006-02-27 License: GPL (GNU General Public License) Price:
1480 downloads
Easy Funktion 6.02

Easy Funktion 6.02


Easy Funktion is a 2D function plotter and equation solver. more>>
Easy Funktion is 2D function plotter software with an equation solver. Easy Funktion has an office-like GUI frontend and features a built-in pocket calculator, calculating with complex numbers (with special extensions for electronics, e.g. capacitor/inductor impedance), a function to export to spreadsheet software, and an advanced formula editor with automatic formatting.
This program alternatively supports an english version of the GUI, but at this time there is no separate english language download available.
In order to activate the english language GUI, do the following:
Open the folder where the program data is installed (/usr/share/easyfunktion). Rename the subfolder de to de_. You may need the root account to do this.
Enhancements:
- Unicode support for Unix.
- An English language GUI with English online help is now available for non-German installations.
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Added: 2007-07-16 License: Free For Educational Use Price:
833 downloads
Q-Audio 2.3

Q-Audio 2.3


Q-Audio is a digital audio interface for Q. more>>
Q-Audio is a digital audio interface for Q. Q-Audio project contains three modules which together provide the basic functionality needed to write digital audio applications.
The audio module implements a (nearly) real-time audio interface on top of the PortAudio library. The sndfile module allows you to access sound files in various formats using libsndfile.
The wave module provides basic operations for creating and manipulating wave data, including operations to convert sample rates, to calculate Fourier transforms, and to display wave data in a GGI visual.
About Q language:
Q is a functional programming language based on term rewriting. Thus, a Q program or "script" is simply a collection of equations which are used to evaluate expressions in a symbolic fashion. The equations establish algebraic identities and are interpreted as rewriting rules in order to reduce expressions to "normal forms". For instance, here is how you define a function sqr which squares its argument by multiplying it with itself:
sqr X = X*X;
Note that, as in Prolog, capitalized identifiers are used to indicate the variables in an equation, which are bound to the actual values when an equation is applied. Equations may also include a condition part, as in the following definition of the factorial function:
fact N = N*fact (N-1) if N>0;
= 1 otherwise;
Functions on structured arguments are defined by "pattern matching". E.g., the product of a list (denoted in Prolog-like syntax) can be computed with these two equations:
prod [] = 1;
prod [X|Xs] = X*prod Xs;
With this definition, the factorial can now also be defined as follows (the notation [1..N], as in Haskell, denotes an arithmetic sequence):
fact N = prod [1..N];
As you can see, the definitions are really just like mathematical equations. The syntax is superficially similar to other modern functional languages like Miranda and Haskell, except that Q is "free-format", i.e., it does not use layout to indicate syntactical structure (thus the semicolon is used to terminate an equation).
Due to its term rewriting heritage, Q goes well beyond most other functional languages in that it also allows you to perform computations with symbolic expressions. For instance, with the definition of the sqr function from above, you will find that sqr (X+1) evaluates to (X+1)*(X+1). This might first look like an arcane feature, but it is actually quite useful, because you can try your definitions with symbolic inputs, too.
Enhancements:
- src/wave.c: minor fixes for compatibility with latest gcc versions
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Added: 2006-02-15 License: GPL (GNU General Public License) Price:
1348 downloads
GREYCstoration 2.5.2.1

GREYCstoration 2.5.2.1


GREYCstoration is an image regularization algorithm which processes an image by locally removing small variations of pixels. more>>
GREYCstoration is an image regularization algorithm which processes an image by locally removing small variations of pixel intensities while preserving significant global image features, such as sharp edges and corners.
The most direct application of image regularization is denoising. By extension, GREYCstoration can also be used to inpaint or resize images.
GREYCstoration is based on state-of-the-art methods using nonlinear multi-valued diffusion PDEs (Partial Differential Equations) for image regularization. This kind of method generally outperforms basic image filtering techniques (such as convolution, median filtering, etc.), classically encountered in painting programs.
Other image denoising plugins are available (for instance, Noise Ninja, Neat Image ) but are not free, and the corresponding algorithms are kept secret.
Enhancements:
- This release consumes far less memory than the previous version (2.4.2), so it can deal with very large images.
- There are now processing modes for 16-bit/components and 32-bit float-valued images, as well as multi-thread support.
- A brand new plug-in for the GIMP is provided.
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Added: 2007-05-10 License: CeCILL (CeCILL Free Software License Agreement) Price:
901 downloads
Mantissa 7.0

Mantissa 7.0


Mantissa is a collection of various mathematical tools aimed towards for simulation. more>>
Mantissa is a collection of various mathematical tools aimed towards for simulation.
Mantissa contains a collection of algorithms, among which:
a small set of linear algebra classes
a least squares estimator
some curve fitting classes
several ordinary differentials equations integrators, either with fixed steps or adaptive stepsize control (see below)
vectors and rotations in a three dimensional space
algebra-related classes like rational and double polynomials
various orthogonal polynomials:
Chebyshev
Hermite
Laguerre
Legendre
some random numbers and vectors generation classes:
Robert M. Ziff four tap shift register (contributed by Bill Maier)
Makoto Matsumoto and Takuji Nishimura Mersenne twister
generators for vectors with correlated components
some basic (min, max, mean, standard deviation) statistical analysis classes
some optimization algorithms using direct search methods:
the Nelder-Mead simplex method
Virginia Torczons multi-directional method
Enhancements:
- For many basic objects provided by Mantissa like Vector3D, Rotation, and the various Polynomial classes, instances are now guaranteed to be immutable.
- This greatly simplifies safe sharing of instances without forcing users to either put severe restrictions on their use of Mantissa classes or make numerous copies just to make sure everything is safe.
- Since the change is a semantic change on the contract of the classes, this version introduces some incompatibilities with respect to previous ones.
- Upgrading to this version is not difficult, though.
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Added: 2006-12-15 License: BSD License Price:
1044 downloads
Qalculate! 0.9.6

Qalculate! 0.9.6


Qalculate! is a multi-purpose desktop calculator for GNU/Linux. more>>
Qalculate! is a multi-purpose desktop calculator for GNU/Linux. Qalculate! project is small and simple to use but with much power and versatility underneath.
Features include customizable functions, units, arbitrary precision, plotting, and a user-friendly interface (KDE or GTK+).
Main features:
- Redesigned GUI with history view in the main window
- Display of as-you-type expression parsing and function hints
- Enhanced completion
- Scaling of result display to vertically fit the window
- Nicer history listing
- Enhanced result display with much nicer parentheses
- Meta modes
- 67 new units: bel (B) and neper (Np), information units such as bit and byte, many convenience units (km/h, deciliter, etc), and more.
- Binary prefixes
- Some new variables and functions
- Fixed help display in new yelp
- Fixed compile with cln-1.1.10
- Fixed regressions in simplification
- Fixed f(x) return type analysis (ex. log(x) represents a real number if x represents a positive). This was by accident unused.
- ...and many more bug fixes and enhancements...
Enhancements:
- Use Lambert W to solve more equations and avoid infinite loop when solving some equations
- More data on elements
- Fix simplification of (1-1/x)^3 and similar
- Fix clumsy mistakes in with prefixes leading to crashes
- Fix parsing of unit expressions (when converting) such as W/(m K)
- Add more exact values for sin() and cos() and avoid floating point underflow by, in approximate mode, checking against the value of pi
- Always input decimal separator sign on keypad separator press
- New units: typographic units, pouce, pied du roi, grams of TNT and tons of TNT
- New functions: lambertW(), addDays(), addMonths(), addYear(), addTime(), isNumber(), isReal(), isRational(), isInteger(), representsNumber(), representsReal(), representsRational(), representsInteger()
- New variable: omega constant
- Other minor fixes and enhancements
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Added: 2007-06-17 License: GPL (GNU General Public License) Price:
860 downloads
eq2png 0.01

eq2png 0.01


eq2png is a simple Perl script to make it painless to produce Portable Network Graphic (PNG) images for OpenOffice Impress. more>>
eq2png is a simple Perl script to make it painless to produce Portable Network Graphic (PNG) images for OpenOffice Impress presentations (or for any other purpose I cant imagine).

Suppose you had a LaTeX snippet in a file named example-equation.tex: To produce the PNG image of this with black foreground and transparent background (the default), youd type:

eq2png example-equation.tex

INSTALLATION:

Youll need ImageMagick, dvips, and Perl.

Just copy the script somewhere into your path, and create a config file if you dont
like the default behavior.

EXAMPLE USAGE:

1) Produce an image of a equation at the command line:
eq2png int{a + b} = c -o intergral.png
If you dont specify an output file, it will default to eq.png
If you add the -b flag, it will make your equation bold (or try to). This is nice for presentations (where sometimes
thin lines dissapear).

2) Produce an image of .tex file snippet. The .tex file should only contain LaTeX code
code you want rendered (not preamble or other such stuff, which gets wrapped around your snippet).
For example, a file equation.tex might include one line, sum_{a}^b = x!.
You can then produce an image of this in the following way:
eq2png equation.tex #defaults to producing a png file with the same name, i.e., equation.png
or,
eq2png equation.tex -o outputfile.png #produce a png file with the name outputfile.png

NOTE: eq2png will only assume a filename is a .tex snippet if it ends in ".tex". So,
eq2png equation.eq
will produce a png image of the string equation.eq (probably not what you want).
To specify that the string is a filename, use the -f flag, e.g.,
eq2png -f equation.eq -o outputfile.png

NOTE: if you want to include LaTeX macros in your equations, just place a file named macros.tex (or symlink)
in your working directory. It will be included in the .tex code generated to produce your png file.

NOTE: if you need to include special LaTeX packages, see the config file stuff below.
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Added: 2005-11-18 License: GPL (GNU General Public License) Price:
1435 downloads
PETSc 2.3.3

PETSc 2.3.3


PETSc is a suite of data structures and routines for the scalable (parallel) solution of scientific applications. more>>
PETSc is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
PETSc library employs the MPI standard for all message-passing communication.
PETSc is easy to use for beginners. Moreover, its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel linear and nonlinear equation solvers that are easily used in application codes written in C, C++, Fortran and now Python.
PETSc provides many of the mechanisms needed within parallel application codes, such as simple parallel matrix and vector assembly routines that allow the overlap of communication and computation. In addition, PETSc includes support for parallel distributed arrays useful for finite difference methods.
Main features:
- Parallel vectors
- scatters (handles communicating ghost point information)
- gathers
- Parallel matrices
- several sparse storage formats
- easy, efficient assembly.
- Scalable parallel preconditioners
- Krylov subspace methods
- Parallel Newton-based nonlinear solvers
- Parallel timestepping (ODE) solvers
- Complete documentation
- Automatic profiling of floating point and memory usage
- Consistent interface
- Intensive error checking
- Portable to UNIX and Windows
- Over one hundred examples
- PETSc is supported and will be actively enhanced for many years.
Enhancements:
- This release adds support for 2D and 3D mesh generation, refinement, partitioning, and distribution.
- It adds support for partitioning based upon arbitrary dimensional entities, e.g. vertices, faces, etc.
- It adds support for FIAT element generation.
- It adds support for higher order elements.
- A Poisson problem example in a separate repository has been added.
- The Hypre interface has been updated to use version 2.0.0.
- The Mumps interface has been updated to use version 4.7.3.
- The fftw interface has been updated to use v3.2alpha2.
- There are numerous bugfixes.
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Added: 2007-06-04 License: Freely Distributable Price:
874 downloads
Modest Ordinary Differential Equation Library 1.0.3

Modest Ordinary Differential Equation Library 1.0.3


Modest Ordinary Differential Equation Library is a C++ library to model rate equations. more>>
Modest Ordinary Differential Equation Library is a C++ library to model rate equations.
MODEL is a numeric simulation library written during my PhD to simulate systems of rate equations describing Vertical Cavity Surface Emitting Lasers (VCSELs). I decided to write one myself after looking at existing libraries and deciding that they were either too complicated to use (having a target user base of mathematicians) or too opaque (i like to know what the code is doing, exactly).
Since most of my programming before has been done in C/C++, what you see here is a C++ library composed of various interacting classes which have the following main functionalities:
deterministic integration of any system of well-behaved differential equations.
- stochastic integration of these systems, with the possibility of specifying the correlations present in the noise
- nonlinear rootfinder, to find stationary solutions
- eigenvalue determination, for stability analysis
- easy time modulation of input parameters
- diverse data collecting classes for data analysis
- Small signal analysis (first order)
The following will be added RSN:
- Fourier transforms, for spectral analysis (although this can be done in an external program)
- Periodic solution finder
It furthermore provides a numerical vector class, vectorfunction classes, LU solver and random generators.
As I developed it using publicly available resources, GNU/Linux and other GPLed software, I decided that it should be GPL as well. However (Oh no, a "however" ! Lets hope it does not invalidate the copyleft), I would very much appreciate it if you let me know if you have used MODEL in any of your applications/simulations/research and provide a reference (this way, I can refer to your work, too).
At the moment, MODEL has the rather arbitrary version number 1.0. Meaning it is useful. Period. Some interfaces (especially the stochastics) might still change, and I would like to add some ieee floating point exception trapping to avoid silly numerical errors.
Enhancements:
- Add features/limitations/changes here
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Added: 2006-09-12 License: GPL (GNU General Public License) Price:
1140 downloads
Eigen 1.0.5

Eigen 1.0.5


Eigen project is a lightweight C++ template library for vector and matrix math, a.k.a. linear algebra. more>>
Eigen project is a lightweight C++ template library for vector and matrix math, a.k.a. linear algebra.
Unlike most other linear algebra libraries, Eigen focuses on the simple mathematical needs of applications: games and other OpenGL apps, spreadsheets and other office apps, etc. Eigen is dedicated to providing optimal speed with GCC.
- Its fixed-size classes are specially optimized for small sizes up to 4, although it is theoretically possible to specialize them to any size. They never cause dynamic memory applications and the simple operations on them are as fast as is possible at least for sizes up to 4 (see below).
- Its dynamic-size classes are more flexible and suitable for larger sizes.
Main features:
- No dependency. Only relies on the C++ Standard Library, and only does so for a few things.
- As a consequence: very good portability.
- Very good performance (tested with GCC, should apply to other compilers as well):
- The fixed-size classes are optimal in the sense that theyre just plain C arrays with methods manipulating them. They never cause dynamic memory allocations. Checked with valgrind.
- The assembly code generated by GCC has been carefully checked to make sure that loop unrolling and function inlining work as expected with "g++ -O2" and "g++ -O3".
- For the loops that GCC fails to unroll (mostly nested loops), we provide hand-unrolled versions for sizes up to 4.
- There is no "virtual" keyword in Eigen.
- Eigen never trades performance for syntactic sugar. When some method introduces a significant language overhead (e.g. returns an object by value), we provide an alternative method doing the same thing faster but without the syntactic sugar.
- Provides easy-to-use classes for solving systems of linear equations.
- Provides easy-to-use functions for linear regression analysis.
- Can perform LU decompositions and use them to invert matrices, compute rank, kernel, etc.
- Integrates nicely with OpenGL:
- Provides functions and classes for projective geometry.
- Stores matrices in column-dominant order, hence matrices can be directly passed between OpenGL and Eigen.
- Uses an OpenGL-like typedef naming scheme, for instance Vector3f for vectors of floats of size 3.
- Robust:
- Only uses algorithms that are guaranteed to work in all cases. For example, the LU decomposition is done with complete pivoting, which means that it works for all square matrices, even singular ones.
- Covered by extensive unit-tests.
- Thread-safe, though thats only as a consequence of staying simple and not trying to do advanced stuff like buffer sharing.
- Floating-point-correct. Eigen has a clear, simple and sound policy with respect to the inherent problems of IEEE754 floating-point arithmetic.
- Fully supports std::complex for matrices and vectors over the complex numbers.
- Is a pure template library and consists only of header files. Thus, using Eigen will only add a build-time dependency to your project.
- Uses standard asserts, controlled as usual by NDEBUG. To achieve optimal performance, turn them off by defining NDEBUG, e.g.
Enhancements:
- This release supports fixed-size classes that are optimized for small sizes of up to four dimensions for 3D geometry and OpenGL.
- Dynamic classes are more flexible and suitable for larger data.
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Added: 2007-06-05 License: GPL (GNU General Public License) Price:
871 downloads
MathStudio 0.7.2-1

MathStudio 0.7.2-1


MathStudio project is an interactive equation editor and step-by-step solver. more>>
MathStudio project is an interactive equation editor and step-by-step solver.
MathStudio is a project aimed at making math-typing, plotting, and symbolic math easier.
Its user can easily input, plot, and save/load math data in various formats (e.g., MathML). Step-by-step resolution makes this a powerful learning tool.
Main features:
- Open Source
- Cross-platform
- Compiler support
- Easy to use
- Simple, extensible
- Intermediate steps
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Added: 2006-10-31 License: GPL (GNU General Public License) Price:
1089 downloads
TuxMathScrabble 4.2

TuxMathScrabble 4.2


TuxMathScrabble is a multi-user math-version of Scrabble for youngsters. more>>
TuxMathScrabble is a math-version of the popular board game for children aged 4-10. The game features drag-and-drop tiles for the user, while Tux moves his own.

The game challenges young people to construct compound equations and consider multiple abstract possibilities.

Dancing penguins come out of the tiles when your move is correct (like a cuckoo-clock). Tux is animated as well.

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Added: 2007-07-28 License: GPL (GNU General Public License) Price:
821 downloads
VULCAN 6.0.0

VULCAN 6.0.0


VULCAN project provides computational fluid dynamics analysis. more>>
VULCAN project provides computational fluid dynamics analysis.
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) offers computational fluid dynamics for subsonic speed through hypersonic turbulent reacting and non-reacting flows on a variety of serial and parallel computational platforms.
The computational cost of propulsion flow analysis is reduced through the use of special turbulent wall treatments, multi-grid methods for elliptic and space marching schemes, and conditioning of the governing equations to reduce numerical stiffness.
Physical modeling capabilities are improved through the inclusion of models for compressibility, Reynolds stress anisotropies, turbulent diffusivity, finite rate chemistry, and turbulence/chemistry interaction effects.
VULCAN can simulate two-dimensional, three-dimensional, or axi-symmetric multi-block problems.
Enhancements:
- This release adds logic to force the correct asymptotic behavior of the turbulence kinetic energy and the turbulence frequency (omega) for surface cell y+ values that are below the log layer portion of the boundary layer.
- It adds the output of reference stagnation conditions and dynamic pressure.
- There are numerous bugfixes, code cleanups, and fixes for setting initial conditions.
- There are minor GUI enhancements.
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Added: 2007-06-02 License: Other/Proprietary License Price:
881 downloads
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