Answer Happy

[70] Q2) Consider the following linear system of equation. d2 x = -Kx dt2 where K = -101 100 100 -101 and x = x(t = 0) = ld and x'(t = 0) = 18 [40] a) Write a Matlab code that solves the IVP with the Backward Euler method. Plot x,(t) and xz(t) in the same figure for 0 < t < 10. (Remark : You may consider the Matlab code template that is provided on LMS.) [30] b) Write a single Matlab code that solves the same IVP given above with the following three functions from the ODE Toolbox of Matlab. Plot xi(t) for all the numerical methods in the same figure. i) ode45 ii) ode23 iii)ode23s
[30] Q1) Consider the following linear system of equation. dx = Ax dt where A = (1 -2] andx = (: [10] a) Solve the ODE system in a) analytically with the initial condition given below. X(t = 0) = 1 [15] b) Solve the initial value problem by HAND using Backward Euler method. Solve for x(t = 1) using a time step size of At = 0.5 [5] c) Evaluate the absolute error between the analytical and numerical solutions both for xi and X2