- GetDP (a General environment for the treatment of Discrete Problems) - http://www.geuz.org/getdp/
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, ...).
- MGNet - http://www.mgnet.org/
Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
- Nonlinear Differential Equations at Glasgow - http://www.maths.gla.ac.uk/~ca/
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.
- The Animated Telegraph equation - http://www.math.ubc.ca/~feldman/demos/demo8.html
This demonstration illustrates the behaviour of solutions of the telegraph equation
- Computational PDEs Unit - http://www.scs.leeds.ac.uk/cpde/
School of Computing, University of Leeds. Research details, publications, software and resources.
- Numerical Methods for Partial Differential Equations - http://www.fusion.kth.se/courses/pde
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.
- PRIDE - http://www.amsta.leeds.ac.uk/Applied/CAGD.dir/PRIDE/index.htm
Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
- Analytic Solution for the Burgers Equation - http://home.usit.net/~cmdaven/burgers.htm
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.
- Table of Laplace Transforms - http://www.vibrationdata.com/Laplace.htm
This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
- Difference Method for Numerical Approximation to Applied Differential Equations. - http://www.geocities.com/b_ward.rm/na.html
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.
- Elliptic Problems with Concentrated Loading - http://www.sci.hkbu.edu.hk/msc/full/billy/billy.html
A web text on the background to the extrapolation method for the numerical solution of elliptic boundary value problems by Kwok Sui-Yuen Billy.
- Finding Green's Functions for ODEs - http://www.mathphysics.com/pde/green/g15.html
A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
- Introduction to Green's Functions - http://www.boulder.nist.gov/div853/greenfn/tutorial.html
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.
- Green's Function Theory - http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node59.html
A set of lecture notes on Green's functions and their applications.
- Linear Mathematics in Infinite Dimensions - http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node2.html
A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
- Partial Differential Equations - http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node24.html
An overview of partial differential equations and their physical applications.
- The Polar Representation Theorem - http://gfm.cii.fc.ul.pt/Members/jr_polar-repr.pdf
An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format.
- PDEase2D 3.0 - http://www.scientek.com/macsyma/pdmain.htm
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.
- Navier-Stokes Type Equations - http://www.coolissues.com/mathematics/Navier-Stokes/nstokes.htm
Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
- Analytical solution for the Korteweg-de Vries equation - http://home.usit.net/~cmdaven/korteweg.htm
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.
- XMorphia - http://www.cacr.caltech.edu/ismap/image.html
A set of graphics and notes intended to show how complex patterns can arise from simple differential equations.
- ODEcalc - http://www.digitalcalculus.com/demos/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 and BVP.
- Osaka University - http://www.sigmath.es.osaka-u.ac.jp/suzuki/ea/ea_eng/
PDE-Analysis research group. Organises the East Asia Symposium on PDE.
- C*ODE*E Archive - http://www.math.hmc.edu/codee/
Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
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