Search for question
Question

Consider the initial value problem \frac{d y}{d t}=f(t), \quad t \in[0, T], \quad y(0)=0 where f(t) is a smooth function of t. We use the following backward Euler's method with step size h: yi+1 = yi+ hf(ti+1). (1) assume that f(t)t. Compute the Aitken estimation for step size h. (Hint:y(0) = 0, so you can compute y explicitly.)=

Fig: 1

Fig: 2

Fig: 3

Fig: 4