T - IfB

Stiff differential equationexample:'y ( t) 15 y( t) , t 0 , y(0) 1Euler:yt t yt t yt O t2( ) () 15 () ( )Becomes unstable if Δt not small enough:Use implicit method (Adams – Moulton):12 2y( t t) y( t) t f ( y( t), t) f ( y( t t), t t) O( t)123Stiff sets of equationsy ' () t K y() t f This system is called() t if matrixThis system is called „stiff“if matrix K has at least onevery large eigenvalue.y ' () t f ( y (),) t tThis system is calledThis system is called „stiff“ ifJacobi matrix has at leastone very large eigenvalue.example:y 998y 1998y'1 1 2y 999y 1999y'2 1 2y (0) 1 , y (0) 11 2Solve with withimplicit method.124