Question 1 only

Problem 2: Theoretical assignment We first consider the following single degree of freedom (SDOF) problem: u + Au = 10 cos(t/10) uo = 100 (1) where the exact solution is given by: 1000A u(t) = 10 - exp + 100 10) cos(t/10) + sin(t/10)] 1 + 100X2 1 + 100X2 (2) and the numerical error is defined as: Numerical - Exact Error = (3) Exact Define the time step length: h = 0.01, and 1. Use Explicit Euler Forward scheme to get u at 1, to and ts and the associated errors (20 points) 2. Use RK 4 to solve this problem to get u at 1, to and to and the associated errors (20 points) 3. Use Implicit Euler Backward to to get u at 1, t2 and ta and the associated errors (20 points)