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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. Includes page about hypercomplex math.
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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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Online course material
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Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
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School of Computing, University of Leeds. Research details, publications, software and resources.
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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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Postscript notes on various topics in differential equations by Bruce Ikenaga.
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EU TMR network coordinated at Oxford Centre for Industrial and Applied Mathematics.
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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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A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
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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, ...).
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Collection of Green's function solutions to canonical differential equations.
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A set of lecture notes on Green's functions and their applications.
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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.
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A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
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Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
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Exact definition of derivation and calculating the relationship of derivatives of related functions.
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Kevin Brown's compilation of postings including many topics in differential equations.
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Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
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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.
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Course notes by Klaus Schmitt at the University of Utah.
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Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
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An overview of partial differential equations and their physical applications.
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This page includes an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
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This demonstration illustrates the behaviour of solutions of the telegraph equation
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An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format.
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Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.
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A set of lecture notes on Poisson's equation. [PDF Format]
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PDEs section of the mathematics e-print arXiv.
