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,

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

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

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

References

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