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Bifurcations, Phase Lines, and Elementary Differential Equations Qualitative approach to autonomous equations. The phase line and the graph of the vector field. Classification of equilibrium points. Bifurcations An application: harvesting Robert L. Devaney May 6, 1995...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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GetDP: a General Environment for the Treatment of Discrete Problems P is a general finite element solver using mixed elements to discretize de Rham-type complexes in one, two and three dimensions. The main feature of GetDP is the closeness between the input data defining discrete problems (written by the user...Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
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MGNet Home Page This is a repository for information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods. These methods are used primarily by scientists and engineers to solve partial differential equations on serial or parallel computers. Multigrid has the...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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Chris Athorne's Home Page This is not a Still Life Perspective Life 2005 Melancholia Resonance Winterreise Light Shade Rhythm Tone...This demonstration illustrates the behaviour of solutions of the telegraph equation
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The Telegraph Equation (animated) This demonstration illustrates the behaviour of solutions of the telegraph equation u_{tt a+b)u_t+abu= c^2 u_{xx} u(0,t 0 u(l,t 0 u(x,0 f(x) u_t(x,0 g(x) In this example c=1, l=10, the intial amplitude consists of one bump centered on x=3. The initial...PDEs section of the mathematics e-print arXiv.
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AP Analysis of PDEs C a regularity of a class of ultraparabolic equations. Liqun Zhang. 20 pages. AP. 20 Oct math.AP/0510402 The Boundary Convergence of the Steady Zero-Temperature-Driven Hard Spheres. A. Sotirov. 8 pages. AP (MP 20 Oct math.AP/0510400 On the Boltzmann Diffusion of...School of Computing, University of Leeds. Research details, publications, software and resources.
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Leeds University CPDE Unit Unit can be contacted via Dr Mark Walkley Email markw@comp.leeds.ac.uk Telephone [UK] 0113 343 5684 [Int 44 113 343 5684 Post Computational PDEs Unit School of Computing University of Leeds Leeds, LS2 9JT, UK Fax [UK] 0113 343 5468 [Int...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
Exact definition of derivation and calculating the relationship of derivatives of related functions.
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Math Unit III: More on the derivative and differential equations More on the derivative and differential equations In the last unit, we discussed how mathematicians and scientists deal with quantities that change in ways other than linearly. The key idea turns out to be the rate of change of the...Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
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PRIDE Download presentation source...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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Analytic Solution for the Burgers Equation Burgers equation is a nonlinear partial differential equation of second order, as follows: It is used in fluid dynamics teaching and in engineering as a simplified model for turbulence, boundary layer behavior, shock wave formation, and mass transport. It has...This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
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Table of Laplace Transforms Laplace transforms are used to solve differential equations. As an example, Laplace transforms are used to determine the response of a harmonic oscillator to an input signal. Dear Visitor, I am raising funds to purchase boats for fishermen in Kakinada,...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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Numerical Analysis of Applied Partial Differential Equations Most real mathematical problems do not have analytical solutions. However, they do have real solutions. In order to obtain these solutions we must use other methods such as graphical representations, or numerical analysis. Numerical analysis is the mathematical method that...Kevin Brown's compilation of postings including many topics in differential equations.
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MathPages: Calculus and Differential Equations Calculus and Differential Equations The Laplace Equation and Harmonic Functions Curvature, Intrinsic and Extrinsic Radial Paths in Schwarzschild Spacetime Analytic Functions, The Magnus Effect, and Wings Fourier Transforms and Uncertainty Propagation of Pressure and Waves The Virial Theorem Integrating the...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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We study the extrapolation method for the numerical solution of elliptic boundary value problems with concentrated loading. Although we do not have theoretical proof, numerical solutions verified that the existence of the asymptotic error expansion at the point of concentrated...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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Green functions for ordinary differential equations. We begin with the case of the first Fredholm alternative. If the equation is in this case, we are guaranteed that it has a unique solution but how to find it? Our method to...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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Tutorial for Green's Functions, Materials Reliability Division, N.I.S.T An example calulation for Green's functions A review of some common techniques used for finding Green's functions A bibliography for reference texts on Green's functions Green's Functions: Basic Concepts Consider a linear differential equation written in the general form (1)...A set of lecture notes on Poisson's equation. [PDF Format]
http://caswww.colorado.edu/cours...AFEM.d/AFEM.Ch03.d/AFEM.Ch03.pdf
A set of lecture notes on Green's functions and their applications.
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The Homogeneous Problem The most basic linear problem consists of finding the null space of The simplest nontrivial extension to differential equations consists of the homogeneous boundary value problem based on the second order differential equation where and is a parameter, with one...A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
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Contents Next: Introduction Up: LINEAR MATHEMATICS IN INFINITE Previous: Preface Index Contents Introduction Infinite Dimensional Vector Spaces Inner Product Spaces Normed Linear Spaces Metric Spaces Complete Metric Spaces Limit of a Sequence Cauchy Sequence Cauchy Completeness: Complete Metric Space, Banach Space,...An overview of partial differential equations and their physical applications.
http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node24.html
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
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.
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PDEase2D 3.0 Main Page D gives you a new way to solve partial differential equations (PDEs) numerically by finite element analysis. Flexible PDEase solves a very wide range of nonlinear problems in heat transfer, solid mechanics, fluid mechanics, groundwater flow, electromagnetics, chemical reaction diffusion,...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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Body It is well known that linear differential equations with real coefficients lead to real dispersion relations only if they consist entirely of even derivatives or they consist entirely of odd derivatives or they consist of imaginary odd derivatives and even...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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Analytic Solution for the Korteweg-de Vries Equation First formulated as part of an analysis of shallow-water waves in canals, it has subsequently been found to be involved in a wide range of physics phenomena, especially those exhibiting shock waves, traveling waves, and solitons. Certain theoretical physics phenomena...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
Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal.
http://www.gwfa.de/math/Fuchs_1996.pdf
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.
http://www.digitalcalculus.com/demos/ODEcalc/
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://home.t-online.de/home/wstripf/
PDE-Analysis research group. Organises the East Asia Symposium on PDE.
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PDE-ANALYSIS GROUP of OSAKA UNIVERSITY The prospectus of the preparatory committee to The East Asia Symposium on PDE Final program of The First East Asia Symposium on Nonlinear PDE (Download dvi file Link to the Second East Asia Differencial Equations Conference Iohara Takao Last modified:...Consortium of ODE Experiments at Harvey Mudd College. Newsletter, graphics, links.
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Welcome to C*ODE*E! E with generous support from the National Science Foundation, published newsletters that provided a regular source of ideas, inspiration, and experiments for instructors of ODEs. The goal of C*ODE*E was to share the rapidly growing wealth of computational instruction techniques...Gives solutions to different types of ordinary differential equations, including linear and nonlinear functions. Many pages use PDF.
http://eqworld.ipmnet.ru/