Find the values of 𝑢(𝑥,𝑡) satisfying the parabolic equation 𝑢𝑡 = 4𝑢𝑥𝑥

Find the values of 𝑢(𝑥,𝑡) satisfying the parabolic equation 𝑢_𝑡 = 4𝑢_𝑥𝑥 and the boundary conditions 𝑢(0,𝑡) = 0 = 𝑢(8,0) and 𝑢(𝑥,0) = 4𝑥 − 𝑥²/2 at the points 𝑥 = 𝑖 ∶ 𝑖 = 0,1,2,…,8 and 𝑡 = 𝑗/8 ∶ 𝑗 = 0,1,2,3,4.

Answer:-