| Directory > Science > Math > Differential Equations XMorphia
A set of graphics and notes intended to show how complex patterns can arise from simple
differential equations.
http://www.cacr.caltech.edu/ismap/image.html
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Analytical solution for the Korteweg-de Vries equation
Provides the general analytic solution for the KdV equation. In one function, the result models
traveling wavetrains, solitary spikes (solitons), and sech-form long waves.
http://home.usit.net/~cmdaven/korteweg.htm
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ODEcalc
An Ordinary Differential Equation (ODE) Calculator. State your equation and boundary or initial
value conditions and it solves your problem. Plots solution, y, and derivative, ydot, versus x.
Solves nth order ODE as IVP & BVP.
http://webs.lanset.com/ecb/ODEcalc.htm
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Navier-Stokes Type Equations
Explicit solutions provided for this particular type of equation and their relations to the heat
equation, Burger's equation, and Euler's equation.
http://www.coolissues.com/mathematics/Navier-Stokes/nstokes.htm
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PDEase2D 3.0
Solves partial differential equations numerically by finite element analysis for use in such
problems as heat transfer, reaction diffusion, solid and fluid mechanics, electromagnetics,
groundwater flow, and quantum mechanics.
http://www.scientek.com/macsyma/pdmain.htm
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The Polar Representation Theorem
An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from
the University of Lisbon. In PDF format.
http://gfm.cii.fc.ul.pt/Members/jr_polar-repr.pdf
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Partial Differential Equations
An overview of partial differential equations and their physical applications.
http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node24.html
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Linear Mathematics in Infinite Dimensions
A set of lecture notes on the mathematical framework that underlies linear systems arising in
physics, engineering and applied mathematics.
http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node2.html
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Green's Function Theory
A set of lecture notes on Green's functions and their applications.
http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node59.html
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Weak and Variational Forms of Poisson's Equation
A set of lecture notes on Poisson's equation. [PDF Format]
http://caswww.colorado.edu/courses.d/AFEM.d/AFEM.Ch03.d/AFEM.Ch03.pdf
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Introduction to Green's Functions
Green's functions play an important role in the solution of linear ordinary and partial
differential equations, and are a key component to the development of boundary integral equation
methods.
http://www.boulder.nist.gov/div853/greenfn/tutorial.html
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Finding Green's Functions for ODEs
A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and
James V. Herod.
http://www.mathphysics.com/pde/green/g15.html
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Elliptic Problems with Concentrated Loading
A web text on the background to the extrapolation method for the numerical solution of elliptic
boundary value problems by Kwok Sui-Yuen Billy.
http://www.sci.hkbu.edu.hk/msc/full/billy/billy.html
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MathPages: Calculus and DiffEq Notes
Kevin Brown's compilation of postings including many topics in differential equations.
http://www.mathpages.com/home/icalculu.htm
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Difference Method for Numerical Approximation to Applied Differential Equations.
This page explains how to use the difference formula of differentials to approximate the
differential equations for applied systems. This method is used when analytical techniques are
unavailable or cause computers to spit out garbage. This difference method is very similar to the
Runge-Kata and Newton's method.
http://www.geocities.com/b_ward.rm/na.html
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Table of Laplace Transforms
This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve
certain differential equations.
http://www.vibrationdata.com/Laplace.htm
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Analytic Solution for the Burgers Equation
Provides the general analytic solution for the Burgers equation in the form of a 4-D commutative
hypercomplex function. The solution exhibits the main dynamic features in a Burgers medium:
propagation of disturbances, shock waves, propagating state change fronts, and solitons. A page is
included to explain the hypercomplex mathematics.
http://home.usit.net/~cmdaven/burgers.htm
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PRIDE
Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
http://www.amsta.leeds.ac.uk/Applied/CAGD.dir/PRIDE/index.htm
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Osaka University
PDE-Analysis research group. Organises the East Asia Symposium on PDE.
http://www.math.sci.osaka-u.ac.jp/handai_kaiseki/
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Math Unit III: More on the derivative and differential equations
Exact definition of derivation and calculating the relationship of derivatives of related
functions.
http://dept.physics.upenn.edu/courses/gladney/mathphys/subsection3_1_1.html
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Stripf's Homepage
A Java Applet to illustrate and solve initial value problems. Uses different numerical methods
(e.g. Runge-Kutta) that can be compared to each other.
http://www.stripf.com
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Differential Equations in Banach Algebras
Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald
Albrecht in Wuppertal.
http://members.aol.com/AlbrechtG4/math3.htm
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Numerical Methods for Partial Differential Equations
Methods such as finite differences, finite elements, fast Fourier transforms, Monte-Carlo and
Lagrangian schemes are discussed in 1D to solve a variety of problems including the advection,
diffusion, Black-Scholes, Burger, Korteweg-DeVries and the Schroedinger equations.
http://www.fusion.kth.se/courses/pde
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Computational PDEs Unit
School of Computing, University of Leeds. Research details, publications, software and resources.
http://www.scs.leeds.ac.uk/cpde/
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arXiv Front: AP Analysis of PDEs
PDEs section of the mathematics e-print arXiv.
http://front.math.ucdavis.edu/math.AP
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Differential Equations in Industry and Commerce
European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.
http://www.maths.ox.ac.uk/ociam/TMR/
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The Animated Telegraph equation
This demonstration illustrates the behaviour of solutions of the telegraph equation
http://www.math.ubc.ca/~feldman/demos/demo8.html
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Nonlinear Differential Equations at Glasgow
The site describes research activities of the differential equations group in the mathematics
department at the university of Glasgow, UK, and provides some resources of a general nature.
http://www.maths.gla.ac.uk/~ca/
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MGNet
Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and
domain decomposition methods.
http://www.mgnet.org/
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GetDP (a General environment for the treatment of Discrete Problems)
A scientific software environment for the numerical solution of integro-differential equations,
open to the coupling of physical problems (electromagnetic, acoustic, thermal, mechanical, ...) as
well as of numerical methods (finite element methods, boundary element and integral methods, ...).
http://www.geuz.org/getdp/
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Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses
Online course material
http://math.bu.edu/DYSYS/ode-bif/ode-bif.html
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