1) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first...

Transcribed Image Text:

1) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first two steps int using At = 0.1 = 12u, + 4u, + 6te"; u, (0) 1 dt du, du, +3 di = 6u, + 9u;; u, (0) = -1 dt 2) An approximation method for the following ordinary differential equation: du =-Âu(t); t e [4,l]. dt with the initial condition u(0) = ug leads to the following one-step formula: 24- 6Ah 24+18Ah+64 h+a'h Show that the local error for the approximation obtained is O(h) when comparing it with Taylor's series of e-ah 1) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first two steps int using At = 0.1 = 12u, + 4u, + 6te"; u, (0) 1 dt du, du, +3 di = 6u, + 9u;; u, (0) = -1 dt 2) An approximation method for the following ordinary differential equation: du =-Âu(t); t e [4,l]. dt with the initial condition u(0) = ug leads to the following one-step formula: 24- 6Ah 24+18Ah+64 h+a'h Show that the local error for the approximation obtained is O(h) when comparing it with Taylor's series of e-ah