partial differential equations
partial differential equations Differential equations that involve two or more independent variables, which in practice are often space and time variables. Because more than one independent variable is present, the “derivatives” that occur are partial derivatives. Such equations are widespread in science and model physical phenomena; they also arise frequently in the form of systems of equations. Simple examples in space and time are given by the heat conduction (or diffusion) equation, u/t = α2u/x2
and the wave equation, 2u/t2 = β2u/x2
where α and β are physical constants. Steady-state phenomena in two space variables are typified by Laplace's equation, 2u/x2 + 2u/y2 = 0
Appropriate initial and boundary conditions must be specified for these equations. The majority of partial differential equations that arise in practice require numerical techniques for their solution, the most successful and widely used being finite-difference and finite-element methods.
and the wave equation, 2u/t2 = β2u/x2
where α and β are physical constants. Steady-state phenomena in two space variables are typified by Laplace's equation, 2u/x2 + 2u/y2 = 0
Appropriate initial and boundary conditions must be specified for these equations. The majority of partial differential equations that arise in practice require numerical techniques for their solution, the most successful and widely used being finite-difference and finite-element methods.
More From encyclopedia.com
Diophantus Of Alexandria , Diophantus of Alexandria
Diophantus of Alexandria
(fl. ad. 250)
mathematics.
We know virtually nothing about the life of Diophantus. The dating of hi… Differential Equations , Differential equations
Differential equations are models of real systems that are believed to change their states continuously, or, to put it more pr… Garrett Birkhoff , Birkhoff was the son of mathematician George David Birkhoff and Margaret Grafius Birkhoff. George Birkhoff, the father, was the first American mathem… George Boole , Boole, George
Boole, George
(b. Lioncoln, England, 1815; d. Cork, Ireland, 1864)
mathematics.
George Boole was the son of John Boole, a cobbler whose… Lysithea , Lysithea (Jupiter X) One of the lesser satellites of Jupiter, with a diameter of 24km. wavelet , wavelet •mallet, palette, pallet, valet •tablet • pamphlet • aglet • anklet •candlelit • hamlet •Caplet, chaplet •lamplit • flatlet • mantlet •haslet…
About this article
partial differential equations
You Might Also Like
NEARBY TERMS
partial differential equations