Use a computer as a computational aid. use the difference equation ui, j + 1 = λui + 1, j + (1 − 2λ)uij + λui − 1, j to approximate the solution of the boundary-value problem ∂2u ∂x2 = ∂u ∂t , 0 < x < 4, 0 < t < 1 u(0, t) = 0, u(4, t) = 0, 0 ≤ t ≤ 1 u(x, 0) = 1, 0 < x ≤ 2 0, 2 < x ≤ 4. use n = 8 and m = 40. (give the approximations obtained for t = 1. round your answers to four decimal places.)