Definition:Boundary Condition
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Definition
Let $\Phi$ be a differential equation to which a particular solution is to be found.
A boundary condition is an equation relating particular values of the dependent and independent variables which the particular solution to $\Phi$ must satisfy.
It is usual for such boundary conditions to correspond to the physical extremities of bodies, aspects of whose internal nature is being modelled by means of $\Phi$.
Also see
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): boundary condition
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): boundary condition
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): boundary condition