Question

Which of these methods is stable for non-linear systems?

(a) Forward Euler method

(b) Backward Euler method

(c) Trapezoidal method

(d) Midpoint rule

This question was posed to me in unit test.

My question is based upon Transient Flows in portion Transient Flows of Computational Fluid Dynamics

Answer 1

The correct choice is (b) Backward Euler method

For explanation I would say: Though the trapezoidal rule is unconditionally stable, it is not the case for non-linear problems. But, the backward Euler method behaves well and smooth for non-linear systems also. They produce smooth results for large time steps too.