4620 Homework 5

You can use any programing language or tool that you want.

1) Compute the LTE of the FD scheme (((Subscript[∇, +t])𝒰)/(Δt))=(((Subscript[δ, x]^2)((Subscript[δ, x]^2)𝒰))/((Δx)^4))+f to approximate (Subscript[u, t])=(Subscript[αu, xxxx])+f

2) Perform a von-Neumann stability analysis of the scheme from (1). On the interval 0<x<0.1 with α=2.4 how many time steps would you need to get a stable computation from t=0 to T=10 with 21 sample points in x.