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Initial Value Problem

An initial value problem is a problem that has its conditions specified at some time $t=t_0$. Usually, the problem is an Ordinary Differential Equation or a Partial Differential Equation. For example,

{\partial^2u\over\partial t^2}-\nabla^2u = f & in ...
u = u_0 & $t=t_0$\cr
u = u_1 & on $\partial\Omega$,\cr}

where $\partial\Omega$ denotes the boundary of $\Omega$, is an initial value problem.

See also Boundary Conditions, Boundary Value Problem, Partial Differential Equation


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

© 1996-9 Eric W. Weisstein