Explicit and implicit methods: Difference between revisions

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In [[mathematics]] and applications, '''explicit and implicit methods''' are approaches tofor [[computer simulation|simulatesimulating]] [[physics|physical]] [[process]]es, or to put it mathematically, 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 next instance in time using the state of the system at the current time, while an implicit method finds it by solving an equation involving both the current system state and the future one. To put it in symbols, if <math>Y(t)</math> is the current system state and <math>Y(t+\Delta t)</math> is the state at the next instance in time (<math>\Delta t</math> is a small time step), then, for an explicit method