Differential Equations
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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
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/
MGNet
Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
http://www.mgnet.org/
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/
The Animated Telegraph equation
This demonstration illustrates the behaviour of solutions of the telegraph equation
http://www.math.ubc.ca/~feldman/demos/demo8.html
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/
arXiv Front: AP Analysis of PDEs
PDEs section of the mathematics e-print arXiv.
http://front.math.ucdavis.edu/math.AP
Computational PDEs Unit
School of Computing, University of Leeds. Research details, publications, software and resources.
http://www.scs.leeds.ac.uk/cpde/
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
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
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
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
Osaka University
PDE-Analysis research group. Organises the East Asia Symposium on PDE.
http://www.math.sci.osaka-u.ac.jp/handai_kaiseki/
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
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
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
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
MathPages: Calculus and DiffEq Notes
Kevin Brown's compilation of postings including many topics in differential equations.
http://www.mathpages.com/home/icalculu.htm
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
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
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
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
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
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
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
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
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
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
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
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
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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