Use a finite difference approach with Delta x 025 to solve

Use a finite difference approach with Delta x = 0.25 to solve d^2/dx^2 + u = x u(0) = 1 u(1) = 2 for 0 lessthanorequalto x lessthanorequalto 1.

Solution

using central difference approch

h=0.25 x=nh u₀=1 u₄=2

(u_n+1-2u_n+u_n-1)/h² +u _n=nh

for n=1;

(u₂-2u₁+ u₀)/0.0625 + u₀=0.25

u₂-2u₁=-1.046875---------------------(1)

for n=2

(u₃-2u₂+ u₁)/0.0625 + u₁=0.5

u₃-2u₂+1.0625u₁ = 0.03125 --------------------(2)

for n=3

(u₄-2u₃+ u₂)/0.0625 + u₂=0.75

2u₃+ u₂ = -2.078125---------------------------(3)

solving equation 1 2 and 3 simultaneously , we get

u₁ = 1.3306 u₂ =1.6144 u₃=1.8463