Stiff equation
In computational mathematics, a stiff equation is an initial value problem u ˙ = f ( u ) , u ( 0 ) = u 0 , t ∈ [ 0 , T ] , {\displaystyle {\dot {u}}=f(u)\,,\qquad u(0)=u_{0}\,,\qquad t\in [0,T]\,,} where f : R d → R d {\displaystyle f:{\mathbb {R} }^{d}\rightarrow {\mathbb {R} }^{d}} , requiring dedicated implicit time stepping methods for its efficient numerical integration. The simplest mathematical characterization of a stiff equation is the necessary condition T d ( d i v u f ) ( u ) ≪ − 1 .