Differential Equations Math Science

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• - Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
  
• - 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
  
• - A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
  
• - 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.
  
• - Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
  
• - Exact definition of derivation and calculating the relationship of derivatives of related functions.
  
• - A set of graphics and notes intended to show how complex patterns can arise from simple differential equations.
  
• - 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.
  
• - 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.
  
• - Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
  
• - An overview of partial differential equations and their physical applications.
  
• - 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.
  
• - Online course material
  
• - 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 Schroed
  
• - 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.
  
• - This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
  
• - A web text on the background to the extrapolation method for the numerical solution of elliptic boundary value problems by Kwok Sui-Yuen Billy.
  
• - Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal.
  
• - PDEs section of the mathematics e-print arXiv.
  
• - A set of lecture notes on Poisson's equation. [PDF Format]
  
• - 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.
  
• - Consortium of ODE Experiments. Newsletter, graphics, links.
  
• - European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.
  
• - 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 met
  
• - 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, bounda
  
• - A set of lecture notes on Green's functions and their applications.
  
• - An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format.
  
• - Kevin Brown's compilation of postings including many topics in differential equations.
  
• - A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
  
• - This demonstration illustrates the behaviour of solutions of the telegraph equation
  
• - School of Computing, University of Leeds. Research details, publications, software and resources.