Implicit time-stepping method
= Implicit time-stepping method
An implicit time-stepping method determines a new solution value through an equation involving that same value. A small-step <contraction mapping> argument often establishes local solvability when the vector field is <Lipschitz continuous>. Examples include the <Backward Euler method>, <implicit Runge-Kutta methods> and implicit <linear multistep methods>. Solvability of the update is a separate issue from <stability of a numerical method>.