Explicit and implicit methods: Difference between revisions

Revision as of 05:46, 11 November 2013

Revision as of 02:41, 12 November 2013

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{{Unreferenced|date=December 2009}}

'''Explicit and implicit methods''' are approaches used in [[numerical analysis]] for obtaining numerical solutions of time-dependent [[ordinary differential equation|ordinary]] and [[partial differential equation]]s, as is required in [[computer simulation]]s of [[Process (science)|physical processes]]. These form a part of [[temporal discretization]] carried out; together with with [[Crank–Nicolson method]].

'''Explicit methods''' calculate the state of a system at a later time from the state of the system at the current time, while '''implicit methods''' find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if <math>Y(t)</math> is the current system state and <math>Y(t+\Delta t)</math> is the state at the later time (<math>\Delta t</math> is a small time step), then, for an explicit method