Initial Value Problem -- from Wolfram MathWorld

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Last updated: Mon Jan 5 2009

Calculus and Analysis > Differential Equations > Ordinary Differential Equations >

Calculus and Analysis > Differential Equations > Partial Differential Equations >

MathWorld Contributors > Cronquist >

Initial Value Problem

An initial value problem is a problem that has its conditions specified at some time . Usually, the problem is an ordinary differential equation or a partial differential equation. For example,

${(partial^2u)/(partialt^2)-del ^2u=f in Omega; u=u_0 t=t_0; u=u_1 on partialOmega,$

(1)

where denotes the boundary of , is an initial value problem.

REFERENCES:

Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C. Computational Differential Equations. Lund, Sweden: Studentlitteratur, 1996.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Initial Value Problems." Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 829, 1992.

CITE THIS AS:

Weisstein, Eric W. "Initial Value Problem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InitialValueProblem.html

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