The transverse displacement u of a point at a distance x from one end and at any time t of a vibrating string satisfies the equation 𝑢𝑡𝑡 = 25 𝑢𝑥𝑥, with the boundary conditions 𝑢(𝑥,𝑡) = 𝑢(5,𝑡) = 0 and the initial conditions
𝑢(𝑥,0) =20𝑥, 0 ≤ 𝑥 ≤ 1
5(5 − 𝑥), 1 ≤ 𝑥 ≤ 5 and 𝑢𝑡(𝑥,0) = 0. Solve this equation numerically up to 𝑡 = 5 taking ℎ = 1,𝑘 = 0.2.
Answer:-
