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Differential equations relate functions of several variables to derivatives of the functions. Such equations are often used in the sciences to relate a quantity to its rate of change.

Calculus	Courses
Difference Equations	Dynamical Systems
Education	Events
Journals	People
Software	Mathematical Physics

• 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.
• 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.
• arXiv Front: AP Analysis of PDEs PDEs section of the mathematics e-print arXiv.
• Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses Online course material
• C*ODE*E Consortium of ODE Experiments. Newsletter, graphics, links.
• Computational PDEs Unit School of Computing, University of Leeds. Research details, publications, software and resources.
• 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.
• Differential Equations in Industry and Commerce European TMR network coordinated at the Oxford Centre for Industrial and Applied Mathematics.
• Differential Equations in Industry and Commerce EU TMR network coordinated at Oxford Centre for Industrial and Applied Mathematics.
• 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.
• Finding Green's Functions for ODEs A brief but technical overview of methods of finding Green's functions. By Evans M. Harrell II and James V. Herod.
• GetDP (a General environment for the treatment of Discrete Problems) 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, ...).
• Green's Function Theory A set of lecture notes on Green's functions and their applications.
• Introduction to Green's Functions 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.
• Linear Mathematics in Infinite Dimensions A set of lecture notes on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics.
• Math Unit III: More on the derivative and differential equations Exact definition of derivation and calculating the relationship of derivatives of related functions.
• MathPages: Calculus and DiffEq Notes Kevin Brown's compilation of postings including many topics in differential equations.
• MGNet Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
• MGNet Information related to multigrid, multilevel, multiscale, aggregation, defect correction, and domain decomposition methods.
• Navier-Stokes Type Equations Explicit solutions provided for this particular type of equation and their relations to the heat equation, Burger's equation, and Euler's equation.
• Nonlinear Differential Equations at Glasgow 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.
• Numerical Methods for Partial Differential Equations 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.
• 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 PDE-Analysis research group. Organises the East Asia Symposium on PDE.
• Partial Differential Equations An overview of partial differential equations and their physical applications.
• PDEase2D 3.0 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.
• PRIDE Products by Rapid Integrated Detailed Engineering. An application of PDEs in engineering design.
• Stripf's Homepage 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.
• Table of Laplace Transforms This page contains an extensive table of Laplace transforms. Laplace transforms are used to solve certain differential equations.
• The Animated Telegraph equation This demonstration illustrates the behaviour of solutions of the telegraph equation
• The Polar Representation Theorem An article covering n-dimensional time-dependent linear Hamiltonian systems. By Jorge Rezende from the University of Lisbon. In PDF format.
• Weak and Variational Forms of Poisson's Equation A set of lecture notes on Poisson's equation. [PDF Format]
• XMorphia A set of graphics and notes intended to show how complex patterns can arise from simple differential equations.

 

 

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