Assess learners' ability to evaluate and select numerical integrators for stiff ordinary differential equations: test understanding of stiffness definitions and indicators, stability concepts (A‑stability, L‑stability), and the trade-offs between explicit and implicit schemes. Include practical evaluation of methods (Backward Euler, BDF, implicit Runge–Kutta, Rosenbrock, exponential integrators), step‑size and error control, Jacobian treatment and preconditioning, sparsity and performance considerations, and require justification of solver choice for given problem scenarios using stability and cost analyses.