You are provided with a semi-explicit index-2 DAE x = f(x, z) 0 = g(x) and you need to write a code to simulate it. Explain the procedure you need to follow, what integration approach you can select (up to 3 options), and how you would deploy them. Provide details showing that you understand your answer. (b) (5 points) How do you need to build the Butcher tableau in order for an IRK method to achieve its highest possible order? (c) (5 points) When should an explicit Runge-Kutta scheme preferred over an implicit one, and vice- versa? What are the pros and cons of both methods? Justify, explain why, be clear and specific. (d) (5 points) You are provided with a model which, when simulated using ODE45 (explicit integrator with error control) performs the integration using very small time steps At. List the possible sources of the problem, and what remedy can be used.