Question

Please do the following, clearly showing/explaining all work. Thank you!

Show that the forward-time central-space scheme (1.3.3) is consistent with the equation (1.1.1).

n+1 1) 2/h

Answer 1

Solution:

Given that,
Given that, V^n + 1_m - V^n_m /K + a V^n_m + n - V^n_m - 1/2h = 0 u_1 au_x = 0 implies V^n + 1_m - V^n_m/K + a V^n_m + n - V^n_m - 1/2h implies 1/2k [V^n + 1_m + V^n + 1_m + 1 - V^n_m + V^n_m + 1] + a/2h [(V^n + 1_m + 1 - V^n + 1_m) + (V^n_m + 1 - V^n_m)] = f^n_m It Consists of one way, wave equation u_t + u_an of and it is a table for all values of 1. \r\n V^n + 1_m - V^n_m/K + a V^n_m + 1 - 3V^n_m + 1 + 3V^n_m - V^n_m - 1/h^3 = f^n_m of V = kh^- 3 is constant when equally therefore The Euler backward scheme for u_t + au_x = f V^n + 1/x_m = V^n_m - ax/2[V^n_m + 1 - V^n_m - 1] + kf^n_m V^m + 1_m = V^n_m - ax/2 [V^n + 1/2_m + 1 - V^n + 1/2_m - 1] + kf^n + 1_m Hence proved