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3651811602

3651811602 - t T ∂ ∂ at t=0 and at x 2 x 3 x 4(b Use...

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Assignment #1 (Mar 1 8 , 2009) ME4906 Numerical Methods for Product Analysis (Deadline for submission: 01 April 2009, 1 0 :00pm) 1. The temperature T of a rod depends on time (t) and position (x) and can be described as a function of t and x: t n e x n t x T 2 2 4 ) sin( ) , ( π = , where n is a positive integer. (a) Calculate t T / ; (b) Calculate 2 2 / x T ; (c) Calculate 2 2 4 x T t T . 2. The temperature T of a rod at time t=0 second and t=0.02 second are tabulated below, where x 1 , x 2 , x 3 , x 4 , x 5 , x 6 label several points in the rod. x 1 =0 x 2 =0.2 x 3 =0.4 x 4 =0.6 x 5 =0.8 x 6 =1.0 t=0 0.0 0.64 0.96 0.96 0.64 0.0 t=0.02 0.0 0.48 0.80 0.80 0.48 0.0 (a) Use forward difference method to calculate
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Unformatted text preview: t T ∂ ∂ / at t=0 and at x 2 , x 3 , x 4 . (b) Use forward difference method to calculate 2 2 / x T ∂ ∂ at t=0 and at x 2 , x 3 , x 4 . (c) Verify by substitution of the results obtained in (a) and (b) that the temperatures listed in the table are solutions to the heat transfer equation 2 2 x T t T ∂ ∂ = ∂ ∂ . 3. Calculate the first derivative of f(x)=sin(x) at x= π /4 using the centre difference scheme with intervals h=0.1, 0.01, 0.005, and 0.002. Identify the order of accuracy of the centre difference scheme....
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