Stiff Differential Equations
A system is stiff when it contains decay timescales differing by orders of magnitude (widely separated eigenvalue magnitudes), forcing explicit methods like Euler and RK4 to take absurdly small steps for stability even after the fast transient has died. Implicit methods (backward Euler, BDF) remain stable at large steps by solving an algebraic equation each step, trading work per step for step count.
This Concept is waiting for its first lesson!
A system is stiff when it contains decay timescales differing by orders of magnitude (widely separated eigenvalue magnitudes), forcing explicit methods like Euler and RK4 to take absurdly small steps for stability even after the fast transient has died. Implicit methods (backward Euler, BDF) remain stable at large steps by solving an algebraic equation each step, trading work per step for step count.
Are you a teacher? Sign in to start contributing.
Sign In