Everything about Separable Partial Differential Equation totally explained
A
separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of
separation of variables. This generally relies upon the problem having some special form or
symmetry. In this way, the PDE can be solved by solving a set of simpler PDEs, or even
ordinary differential equations (ODEs) if the problem can be broken down into one-dimensional equations.
(This shouldn't be confused with the case of a separable ODE, which refers to a somewhat different class of problems that can be broken into a pair of
integrals; see
separation of variables.)
Example
For example, consider the time-independent
Schrödinger equation
» . (More generally, the separable cases of the Schrödinger equation were enumerated by Eisenhart in 1948.)
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