Initial-value problem

From Glossary of Meteorology

initial-value problem

A class of problems that have solutions determined by time integration of a set of differential equations from some initial state.

For example, the equilibrium state of a damped linear system can be obtained by time- integrating the governing set of equations until a steady state is reached. A short-term NWP forecast is another example of an initial-value problem.
See transient problem;
compare boundary-value problem.