= Problem 1. Use the Crank-Nicolson Method to solve the equation Tut = Uzx for 0 < x <1,0

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Problem 1 Use The Crank Nicolson Method To Solve The Equation Tut Uzx For 0 X 1 0 T 1 With The Initial And Boun 1 (99.71 KiB) Viewed 23 times

= Problem 1. Use the Crank-Nicolson Method to solve the equation Tut = Uzx for 0 < x <1,0 <t<1 with the initial and boundary conditions that follow. u(x,0) = sin au 0 < x < 1 u(0, t) = 0 0 <t<1 u(1,t) = 0 0 <t<1 The exact solution is u(x, t) Make a table of the exact value, the approximate value, and error at (x, t) = (0.3,1) for step sizes h= k = 0.1,0.05,0.025. = e -art sin I. = u(0.3,1) w(0.3, 1) error 0.00000601 h 0.1 0.05 0.025 k 0.1 0.05 0.025 Consider the equation nut Uxx for 0 < x < 1, 0 < t < 1 with the initial and boundary conditions that follow. u(x,0) = cos TX 0 < x < 1 0 <t<1 u(1,t) = 0 <t<1 The exact solution is u(x, t) = e Use the Crank-Nicolson Method to solve the problem. Make a table of the exact value, the approximate value, and error at (x, t) = (0.3,1) for step sizes h = k = 0.1, 0.05, 0.025. u(0,t) = e-at -e-at at COS C. —