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Differential Equations

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Differential Equations Sites

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1. arXiv Front: AP Analysis of PDEs
PDEs section of the mathematics e-print arXiv.

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2. C*ODE*E Archive
Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.

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3. 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.

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4. Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses
Online course material

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5. Differential Equations in Banach Algebras
Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal. [PDF]

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6. 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.

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7. 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.

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8. Computational PDEs Unit
School of Computing, University of Leeds. Research details, publications, software and resources.

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9. Differential Equations in Industry and Commerce
European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.

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10. 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.

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