Use a computer as a computational aid. Use the difference equation ujj+1 = Au¡+1,j + (1 − 2λ)u¡j + λu₁-1,j to approximate the solution of the boundary-value problem a²u au = əx² at " u(0, t) = 0, u(8, t) = 0, 0 ≤ts1 u(x, 0) = u(4.00, 1) = u(5.00, 1) = u(6.00, 1) = u(7.00, 1) = 0 < x < 8,0 < t < 1 1, 0, 0 < x≤ 4 4 < x≤ 8. Use n = 8 and m = 40. (Give the approximations obtained for t= 1. Round your answers to four decimal places.) u(1.00, 1) u(2.00, 1) = u(3.00, 1) =

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