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Initial-value problems (IVPs), where the solution u and its derivatives (often with respect to time) are specified in one point (in time) so that u(0) and
 are known, so the system is assumed to start at a fixed initial point. The Global Equations node in COMSOL Multiphysics supports such IVPs described with an equation in the following form:  , including initial values for u and its derivatives. |
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Boundary-value problems (BVPs), where the solution u has specified values at a pair of points such as u(0) and u(1); that is, the points 0 and 1 are regarded as boundary points of the domain for the problem. In COMSOL Multiphysics, you can specify such a BVP as a stationary 1D PDE, where the 1D interval represents the independent variable and the u is the dependent variable in the interval.
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