partial differential equations
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.
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