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Topic: Partial differential equation

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In the News (Fri 14 Jun 19)

  Partial differential equation - Wikipedia, the free encyclopedia
Partial differential equations are used to formulate and solve problems that involve unknown functions of several variables, such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, elasticity, or more generally any process that is distributed in space, or distributed in space and time.
The Schrödinger equation is a PDE at the heart of non-relativistic quantum mechanics.
In the WKB approximation it is the Hamilton-Jacobi equation.
en.wikipedia.org /wiki/Partial_differential_equation   (2676 words)

 PlanetMath: differential equation   (Site not responding. Last check: 2007-10-22)
A differential equation is an equation involving an unknown function of one or more variables, its derivatives and the independent variables.
In a delay differential equation (DDE), the unknown function depends on the state of the system at some instant in the past.
This is version 8 of differential equation, born on 2002-05-30, modified 2005-05-09.
planetmath.org /encyclopedia/PartialDifferentialEquation.html   (432 words)

 Method for preparing a simulation program - Patent 4841479
The partial regions of the object region are denominated, as indicated in 21 of FIG.
The data of partial differential equation and boundary condition 2, the data of region 3 and the data of difference rule 4 are kept in the intermediate table respectively as the data of equation 503, the data of the shape of the region 502 and the intermediate data of difference rule 501.
For example, in the x-direction it is divided at the boundary of the equation a and in the y-direction at the boundary between the equations a and b.
www.freepatentsonline.com /4841479.html   (3596 words)

 Definitions of Partial Differential Equations
A partial differential equation is an equation that involves an unknown function and its partial derivatives.
Equation (2.1) is the one dimensional wave equation, equation (2.2) is the one dimensional heat (or diffusion) equation and equation (2.3) is the two dimensional Laplace equation.
However, unlike second order ordinary differential equations where there are two linearly independent solutions and two arbitrary constants, linear partial differential equations may well have an infinte number of linearly independent solutions and we may have to add together solutions involving an infinite number of constants.
www-solar.mcs.st-and.ac.uk /~alan/MT2003/PDE/node10.html   (350 words)

 Partial differential operators.
In thinking of partial differential equations, it is a common practice to carry over the language that has been used for matrix or ordinary differential equations in as far as possible.
) = 0"> is a parabolic partial differential equation,
We choose the constants as the coefficients for the partial differential equations
www.mathphysics.com /pde/green/ch19wr.html   (4391 words)

 Elliptic Partial Differential Equation   (Site not responding. Last check: 2007-10-22)
Distributed memory implementation of elliptic partial differential equations in...
Backward stochastic differential equations and partial differential equations wi...
Parameter identification for an elliptic partial differential equation with dist...
www.scienceoxygen.com /math/501.html   (357 words)

 Applied Partial Differential Equations   (Site not responding. Last check: 2007-10-22)
Along a characteristic curve the partial differential equation reduces to an ordinary differential equation.
The reduction of quasi-linear second order partial differential equations in two variables to canonical form is discussed.
A partial differential equation becomes an ordinary differential equation in the similarity variable.
www.cam.wits.ac.za /indus_math/apde.html   (218 words)

 Method for automatically generating a simulation program for a physical phenomenon governed by a partial differential ...
Simultaneous linear equations comprising the linear equations derived for various nodes are solved to determine the unknown values F at the respective nodes.
Such simulation is effective to the design of a circuit or a device but the matrix equation to be solved changes depending on the partial differential equation, the boundary conditions, the shape of the area and the procedure of numeric calculation.
When the partial region to which the designation formula or the boundary condition formula is to be applied is to be designated, the name thereof is not entered but the displayed partial region is picked up so that the name of the partial region already inputted is quoted.
www.freepatentsonline.com /5148379.html   (14829 words)

 PlanetMath: Beltrami differential equation   (Site not responding. Last check: 2007-10-22)
is a measurable function, then the partial differential equation
Cross-references: imaginary parts, real, terms, complex conjugate, partial derivatives, conformal, conformal mapping, quasiconformal mapping, solution, domain, bound, uniform, partial differential equation, measurable function
This is version 5 of Beltrami differential equation, born on 2004-02-10, modified 2004-06-10.
planetmath.org /encyclopedia/BeltramiDifferentialEquation.html   (131 words)

 Partial Differential Equation Lab
Partial differential equations (PDEs) occur in many different areas of physics, ranging from quantum mechanics to general relativity, and including fields like hydrodynamics and electrodynamics.
Many of these equations can be cast as quasi-linear parabolic equations, in which there is a first order derivative in one dimension, together with higher-order derivatives in the others.
These types of equation, which are called quasi-linear if the derivative terms are all linear in the equation, are extremely common.
www.physics.uq.edu.au /people/cochrane/phys3071/phys3071Notes/node1.html   (438 words)

 Partial Differential Equation
Partial differential equations (PDE) have been widely used in image restoration (denoise, inpainting or fill-in, super-resolution), and image analysis (segmentation and tracking objects).
Secondly the PDEs must be adapted to the statistical properties of the image ensemble.
Then PDEs are derived and shown to be much more general than the popular non-linear diffusion equations for edge preserving (Perona and Malik).
www.stat.ucla.edu /centers/civs/PDE/pde.html   (488 words)

 Partial Differential Equations
The model is a system of three non-linear ordinary differential equations, and is now studied in introductory calculus courses.
The partial differential equation of a vibrating membrane in rectangular and in polar coordinates is
The heat equation is a diffusion equation like the SIR model, and we can get approximate numerical solutions the same way, using Euler's method.
maven.smith.edu /~callahan/ili/pde.html   (1164 words)

 detools::characteristics -- characteristics of partial differential equation
the differential equation: an element of a domain generated with the constructor
As the characteristic system is an in general nonlinear system of ordinary differential equations, this can be a very hard task.
There should be exactly one condition for each independent and dependent variable of the original partial differential equation.
www.mupad.de /doc/25/de/detools/characteristics.shtml   (244 words)

 Two dimensional first order partial differential equation   (Site not responding. Last check: 2007-10-22)
The object is to start with the known boundary condition at t=0 (the bottom of the picture) and to proceed upwards in time while satisfying the boundary conditions at x=0,t=1,2,...
This set of equations involves the j-1,j,j+1 elements of the matrix only and is know as tri-diagonal.
t in the time step by using the difference equation as an estimate of the time derivative at one end or the other.
www.phys.ufl.edu /~coldwell/class2K/diffeqns/Partdiff.htm   (972 words)

 Partial Differential Equations   (Site not responding. Last check: 2007-10-22)
Schaum's Outline of Partial Differential Equations (McGraw-Hill) doi:10.1036/007...
The MathWorks - Partial Differential Equation Toolbox - Solve and analyze partia...
A First Course in Partial Differential Equations with Complex Variables...
www.scienceoxygen.com /math/490.html   (239 words)

 Examples (Partial Differential Equation Toolbox)
The last problem, a minimal surface problem, is nonlinear and illustrates the use of the nonlinear solver.
The problems are solved using both the graphical user interface and the command-line functions of the PDE Toolbox.
Note that the coefficients of the elliptic PDE are constants (c = f = 1, a = 0) for this simple case.
faculty.biu.ac.il /~htmldoc/matlabaix/toolbox/pde/2exampl2.html   (724 words)

 Partial differential equation example
The following technique makes use of the fact that the equation is actually Laplace's equation and leads to a much smaller
The coefficients are then found by solving the overdetermined set of equations
Once the coefficients have been determined, the approximate solution is defined everywhere on the domain.
ccrma-www.stanford.edu /~jos/matdoc/Partial_differential_equation_example.html   (592 words)

 Tutorial (Partial Differential Equation Toolbox)   (Site not responding. Last check: 2007-10-22)
The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time.
An overview of the features, functions, and uses of the PDE Toolbox.
Description of the use of the Finite Element Method (FEM) to approximate a piecewise linear function and the use of FEM techniques to solve more general problems.
www-rohan.sdsu.edu /doc/matlab/toolbox/pde/1tut.html   (112 words)

 EG3004 – Engineerring Analysis and Methods
The partial differential equation is the one-dimensional heat conduction equation:
The partial differential equation is the one-dimensional wave equation:
and the subsidiary conditions are (note that there are no initial conditions given here, so that it would be impossible to obtain a complete solution of the partial differential equation):
www.abdn.ac.uk /~eng030/eg3004/tut6solns.htm   (49 words)

 Message Passing: Code Development
This lecture discusses a simple problem which illustrates the use of the MPI library to parallelize a partial differential equation.
The objective of this lecture is to go over a simple problem that illustrates the use of the MPI library to parallelize a partial differential equation (PDE).
The Laplace problem is a simple PDE and is found at the core of many applications.
www.sc-2.psc.edu /workshop/jan01/Code_Development/Code_Development.html   (1526 words)

 assemb (Partial Differential Equation Toolbox)
describes the boundary conditions of the PDE problem.
The toolbox can also handle systems of partial differential equations over the domain
For a boundary in a scalar PDE (N = 1) with Neumann boundary condition (M = 0)
faculty.biu.ac.il /~htmldoc/matlabaix/toolbox/pde/assemb.html   (554 words)

 Tutorial (Partial Differential Equation Toolbox)   (Site not responding. Last check: 2007-10-22)
The PDE Toolbox uses the Constructive Solid Geometry (CSG) model paradigm for the modeling.
in the plane over which the differential equation is solved.
The operators +, the set union operator, and *, the set intersection operator, have the same precedence.
www.weizmann.ac.il /matlab/toolbox/pde/1tut14.html   (292 words)

 Computing optimal control with a hyperbolic partial differential equation   (Site not responding. Last check: 2007-10-22)
We present a method for solving a class of optimal control problems involving hyperbolic partial differential equations.
A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given.
Fast automatic differentiation is applied to calculate the exact gradient of the discretized problem so that existing optimization algorithms may be imposed on the problem.
anziamj.austms.org.au /V40/part2/Rehbock.html   (163 words)

 The Partial Differential Equation Toolbox   (Site not responding. Last check: 2007-10-22)
The Partial Differential Equation Toolbox extends the MATLAB Technical Computing Environment for the study and solution of PDEs in two space dimensions (2-D) and time.
The PDE Toolbox provides a set of command line functions and an intuitive graphical user interface for preprocessing, solving and postprocessing generic 2-D PDEs using the Finite Element Method (FEM).
The toolbox also provides automatic and adaptive meshing capabilities, and a suite of eight application modes for common PDE application areas such as heat transfer, structural mechanics, electrostatics, magnetostatics, and diffusion.
www.tu-harburg.de /rzt/tuinfo/software/numsoft/matlab/pde.html   (108 words)

 Adaptive Numerical Solution of Partial Differential Equation
there are many different types of PDE's available that has been explored and methods for finding the solutions for PDE's of that form have been discovered...
The objective of Adaptive solution is to appropriat flexible griding of Domain of solution, in order to time and memory efficient solving of PDE.
Because, suppose if u are to design a complete partial differential equation solver, then the input wen given, u are to analyse the structure of the equation and then "choose" the methods available!
www.edaboard.com /ftopic99746.html   (285 words)

Examiner: C. In modelling many physical processes such as fluid transfer, transport phenomena in fluids and solids the resulting partial differential equations are not usually amenable to direct analytic solution.
This unit introduces computational numerical techniques which are available for a wide range of partial differential equation models.
equation models for a wide range of applications including
www.usq.edu.au /unit-2000/fullspec/64422s1d.htm   (299 words)

 FAQTs - Knowledge Base - View Entry - Math: Calculus: Differential equation: Partial: Link: Overview: Can you give an ...
faqts : Science : Mathematics : Calculus : Differential equation : Partial
Math: Calculus: Differential equation: Partial: Link: Overview: Can you give an overview of links?
--- --- Internet: see also: --- Math:Calculus:Differential equation:Partial:History:Who founded theory partial differential equation http://www.faqts.com/knowledge_base/view.phtml/aid/35533/fid/813 --- Math: Calculus: Definition: What is the definition of a partial differential equation?
www.faqts.com /knowledge_base/view.phtml/aid/35621   (159 words)

 FlexPDE finite element model builder for Partial Differential Equations
The Original Unlimited Scripted Multi-Physics Finite Element Solution Environment for Partial Differential Equations is now more powerful than ever!
From stress analysis to chemical reaction kinetics to stock option pricing, mathematical modeling of real world systems is dominated by partial differential equations.
FlexPDE addresses the mathematical basis of all these fields by treating the equations rather than the application.
www.pdesolutions.com   (126 words)

 Tutorial (Partial Differential Equation Toolbox)   (Site not responding. Last check: 2007-10-22)
Working with the system matrices and vectors produced by
When solving the same equation for different loads or boundary conditions, it pays to assemble the stiffness matrix only once.
Point loads on a particular node can be implemented by adding the load to the corresponding row in the right side vector.
www.eecs.umich.edu /dco/faq/matlab-6.5/help/toolbox/pde/1tut21.html   (280 words)

 Basic Partial Differential Equation   (Site not responding. Last check: 2007-10-22)
Topics not usually found in books at this level include but examined in this text:
convergence of numerical solutions of PDEs and implementation on a computer
The text requires some knowledge of calculus but none on differential equations or linear algebra.
www.ramex.com /title.asp?id=4007   (133 words)

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