Explicit and implicit methods: Difference between revisions

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In [[applied mathematics]], '''explicit and implicit methods''' are approaches used in [[computer simulation]]s of [[physics|physical]] [[Process (science)|processes]], or in other words, they are [[numerical analysis|numerical methods]] for solving time-variable [[ordinary differential equation|ordinary]] and [[partial differential equation]]s.

Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while an implicit method finds it by solving an equation involving both the current state of the system and the later one. To put it in symbolsMathematically, 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

: <math>Y(t+\Delta t) = F(Y(t))\,</math>

while for an implicit method one solves an equation