Consider the heat equation, Ut = Uzz, u(t,0)=0, u(t, 1) = 0, u(0, 2) = sin(x),...
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Consider the heat equation, Ut = Uzz, u(t,0)=0, u(t, 1) = 0, u(0, 2) = sin(x), t>0, 0<x< 1, (a) Verify that u(t, x) = e-t sin(x) is a solution. (b) Plot, on the same axes, the exact solution as a function of r for the times t = 0.001,0.01,0.1. (c) Plot the surface of the exact solution as a function of 2 € [0, 1] and t€ [0.0.1] using 22 and 11 points respectively. (d) Plot, on the same axes, the numerical solution as a function of r at time T = 0.1 using 20 internal grid points and m = 5, 10, 20 time steps. Use the Crank-Nicolson method. List the script file you actually use. Consider the heat equation, Ut = Uzz, u(t,0)=0, u(t, 1) = 0, u(0, 2) = sin(x), t>0, 0<x< 1, (a) Verify that u(t, x) = e-t sin(x) is a solution. (b) Plot, on the same axes, the exact solution as a function of r for the times t = 0.001,0.01,0.1. (c) Plot the surface of the exact solution as a function of 2 € [0, 1] and t€ [0.0.1] using 22 and 11 points respectively. (d) Plot, on the same axes, the numerical solution as a function of r at time T = 0.1 using 20 internal grid points and m = 5, 10, 20 time steps. Use the Crank-Nicolson method. List the script file you actually use.
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Answer rating: 100% (QA)
To verify and plot the solutions of the heat equation well need to use numerical methods Specifically well use the CrankNicolson method to solve the e... View the full answer
Related Book For
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis
Posted Date:
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