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 Archive
Consortium of ODE Experiments at Harvey Mudd College. 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 Banach Algebras
Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal.
Differential Equations in Industry and Commerce
European TMR network coordinated at the 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.
Results: 1 2 Next
