Consider a model equation in a domain [0,1]: with the initial value given by at...
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Consider a model equation in a domain [0,1]: with the initial value given by ди at + du ????x u(x,0) = µu (u − 1)(u— 1½) 1 0 if x ≤ 0.3 if x > 0.3 The exact solution is given by u(x,t) = u(x-t,0). Obtain solution to this model equation at t= 0.3 for = 1, 5, 50, 500, and 1000. 1. Compute your answer using a linearized implicit method and plot against the exact solution. 2. Try using any 1st order explicit method and any 2nd order explicit method. Compare against the exact solution. is a stiffness coefficient, which is analogous to Reynolds or Damkohler number. State what you have observed on the stiffness of ordinary differential equations. Consider a model equation in a domain [0,1]: with the initial value given by ди at + du ????x u(x,0) = µu (u − 1)(u— 1½) 1 0 if x ≤ 0.3 if x > 0.3 The exact solution is given by u(x,t) = u(x-t,0). Obtain solution to this model equation at t= 0.3 for = 1, 5, 50, 500, and 1000. 1. Compute your answer using a linearized implicit method and plot against the exact solution. 2. Try using any 1st order explicit method and any 2nd order explicit method. Compare against the exact solution. is a stiffness coefficient, which is analogous to Reynolds or Damkohler number. State what you have observed on the stiffness of ordinary differential equations.
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1 Solution at t 03 for 1 5 50 500 and 1000 For t 03 the exact solution for different values of x is given below x ux 03 1 u103 0 u07 0 5 u503 0 u47 0 ... View the full answer
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Essentials of Marketing
ISBN: 978-0078028885
13th edition
Authors: William D. Perreault, Joseph P. Cannon
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