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Topic: Initial value problem

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Boundary value problem

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	PlanetMath: initial value problem
		An initial value problem is then a differential equation (ordinary or partial, or even a system) which, besides of stating the relation among the derivatives, also, by giving the initial conditions, specifies the values of the unknowns at some point.
		In fact, one of the main problems in the theory of differential equations is to determine what sort of initial conditions will single out a unique solution of a given differential equation.
		This is version 6 of initial value problem, born on 2003-10-24, modified 2006-02-22.
	planetmath.org /encyclopedia/InitialValueProblem.html (340 words)

	Initial value problem - Wikipedia, the free encyclopedia
		In mathematics, an initial value problem is a statement of a differential equation together with specified value of the unknown function at a given point in the domain of the solution.
		The proof of this theorem proceeds by reformulating the problem as an equivalent integral equation.
		Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
	en.wikipedia.org /wiki/Initial_value_problem (390 words)

	Boundary value problem - Wikipedia, the free encyclopedia
		In mathematics, a boundary value problem consists of a differential equation and the initial or boundary values required to solve the equation.
		Among the earliest boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation); the solution was given by the Dirichlet principle.
		Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
	en.wikipedia.org /wiki/Boundary_value_problem (635 words)

	PlanetMath: Cauchy initial value problem
		Also, depending on the topics, the name chosen for the function and for the variable, can change.
		"Cauchy initial value problem" is owned by paolini.
		This is version 9 of Cauchy initial value problem, born on 2005-01-19, modified 2006-07-25.
	planetmath.org /encyclopedia/CauchyInitialValueProblem.html (178 words)

	Introduction to Differential Equations, part 2
		This second condition is called an initial condition -- the value of dependent variable (in this case S) at the first value of the independent variable (in this case t) under consideration.
		A differential equation together with an initial condition is called an initial value problem.
		A solution to an initial value problem is a solution to the differential equation that also satisfies the initial condition.
	www.math.duke.edu /education/postcalc/ode/ode2.html (429 words)

	9.5 The initial boundary value problem (Site not responding. Last check: 2007-11-02)
		This leads to the consideration of initial boundary value problems.
		It is not so natural to consider such problems in the case of the Einstein equations since in that case there are no physically motivated boundary conditions.
		Since boundary conditions come up quite naturally when the Einstein equations are solved numerically, due to the need to use a finite grid, the results of [107] are potentially important for numerical relativity.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2002-6/node40.html (203 words)

	[No title]
		A lot of the equations that you work with in science and engineering are derived from a specific type of differential equation called an initial value problem.
		Using the initial data, plug it into the general solution and solve for c.
		= -4sin 2t, initial velocity v (0) = 2, and the initial position of the body as s (0) = -3.
	faculty.eicc.edu /bwood/math150supnotes/supplemental19.htm (279 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		We study the initial value problem for actions whose non-locality is{open_quotes}maximal{close_quotes} in the sense that there is no dependence upon the separation between points.
		We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations.
		It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=567089 (287 words)

	VTK: vtkInitialValueProblemSolver Class Reference (via CobWeb/3.1 planetlab-3.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		Integrate a set of ordinary differential equations (initial value problem) in time.
		Given initial values, xprev, initial time, t and a requested time interval, delT calculate values of x at t+delTActual (xnext).
		An estimated value for the error is returned (by reference) in error.
	noodle.med.yale.edu.cob-web.org:8888 /vtk/classvtkInitialValueProblemSolver.html (794 words)

	Dictionary of Technical Terms for Aerospace Use - I (via CobWeb/3.1 planetlab-3.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		Any of those variables of a problem, chosen according to convenience, which may arbitrarily be specified, and which then determine the other or dependent variables of the problem.
		A dynamical problem whose solution determines the state of a system at all times subsequent to a given time at which the state of the system is specified by given initial conditions.
		In meteorology, a departure from the usual decrease or increase with altitude of the value of an atmospheric property; also, the layer through which this departure occurs (the inversion layer), or the lowest altitude at which the departure is found (the base of the inversion).
	roland.grc.nasa.gov.cob-web.org:8888 /~dglover/dictionary/i.html (6483 words)

	initial value problem (Site not responding. Last check: 2007-11-02)
		i know how to do the question but my problem is just i dont know how to get all the x's on one side and the y's on the other.
		I probably gave away the real trick to the problem, which was the proper rearrangment of the equation.
		I think 40% of the problem was the getting the 2nd and 3rd lines, 50% of the problem was lines 4-7, and 10% was the rest.
	www.physicsforums.com /showthread.php?t=26365 (420 words)

	Main Results and Relation to Gelfand-Yaglom's Initial-Value Problem
		Here we present an even more direct method, by which we express the result in terms of solutions of Gelfand-Yaglom's initial-value problem for Dirichlet boundary conditions, and of a dual problem for periodic and antiperiodic boundary conditions.
		In terms of the same functions, the general solution of the inhomogeneous initial-value problem (42) can be seen to have the form
		For this purpose we introduce another homogeneous initial-value problem whose boundary conditions are dual to Gelfand and Yaglom's in (41):
	www.physik.fu-berlin.de /~kleinert/kleiner_re264/node4.html (510 words)

	Test Set for Initial Value Problem Solvers: Introduction (Site not responding. Last check: 2007-11-02)
		Both engineers and computational scientists alike will benefit greatly from having a standard test set for Initial Value Problems (IVPs) which includes documentation of the test problems, experimental results from a number of proven solvers, and Fortran subroutines providing a common interface to the defining problem functions.
		Engineers will be able to see at a glance which methods will be most effective for their class of problems.
		Researchers will be able to compare their new methods with the results of existing ones without incurring additional programming workload; they will have a reference with which their colleagues are familiar.
	pitagora.dm.uniba.it /~testset (226 words)

	Listbox problem - taking initial value from database - ASP
		to be edited, the value is displayed as a '1' and not a 'yes'.
		> to be edited, the value is displayed as a '1' and not a 'yes'.
		> > to be edited, the value is displayed as a '1' and not a 'yes'.
	www.thescripts.com /forum/thread51782.html (755 words)

	Solving systems by finding eigenvalues and eigenvectors
		The initial value problem consists in finding a solution to (2) that satisfies an initial condition
		Determining the integration constants from linear algebraic system (14) and inserting in (12) one obtains the solution to initial value problem (2), (13).
		Note: Steps 3-4 must be filled only for initial value problems.
	www.cs.ut.ee /~toomas_l/linalg/dv_2/node5.html (267 words)

	Table of Contents for Partial Differential Equations: Analytical Solution Techniques
		Initial- and Boundary-Value Problems on the Semi-Infinite Domain; Green's Functions
		3.5 Initial- and Boundary-Value Problems on the Semi-Infinite Interval; Green's Functions
		Initial- and Boundary-Value Problems on the Finite Interval; Green's Functions
	www.amath.washington.edu /research/books/Kevorkian/PDE/toc.html (453 words)

	Initial Value Problem -- from Wolfram MathWorld
		An initial value problem is a problem that has its conditions specified at some time
		SEE ALSO: Boundary Conditions, Boundary Value Problem, Initial Conditions, Partial Differential Equation.
		Weisstein, Eric W. "Initial Value Problem." From MathWorld--A Wolfram Web Resource.
	mathworld.wolfram.com /InitialValueProblem.html (104 words)

	DC MetaData for: The Algebro-Geometric Toda Hierarchy Initial Value Problem for Complex-Valued Initial Data (Site not responding. Last check: 2007-11-02)
		DC MetaData for: The Algebro-Geometric Toda Hierarchy Initial Value Problem for Complex-Valued Initial Data
		Abstract: We discuss the algebro-geometric initial value problem for the Toda hierarchy
		To this effect we develop a new algorithm for constructing stationary complex-valued algebro-geometric solutions of the Toda hierarchy, which is of independent interest as it solves the inverse
	www.esi.ac.at /Preprint-shadows/esi1767.html (273 words)

	The INITIAL VALUE PROBLEM (IVP) (via CobWeb/3.1 planetlab-3.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		The first part will consider the ``initial value problem.'' (IVP) in detail.
		The second part will present the ``boundary value problem'' (BVP) in a cursory way (see notes for 575B course, where we use variational methods to recast the BVP for its numerical solution, a powerful and elegant analytical technique that leads to a host of important numerical schemes).
		Errors in the Numerical Approximation of the IVP
	www.physics.arizona.edu.cob-web.org:8888 /~restrepo/475B/Notes/source/node3.html (195 words)

	Initial Value Problem (Site not responding. Last check: 2007-11-02)
		then to solve for C you plug in the given values for v and t and solve.
		Then because you want s(t), you integrate once more.
		and you solve for C again with the given initial values of s and t.
	www.physicsforums.com /showthread.php?threadid=98208 (465 words)

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