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  3. a for ux t defined on the domain of 0...

Question: a for ux t defined on the domain of 0...

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(a) For ux, t) defined on the domain of 0 x and 20, solve the PDE au 2u at ax2 with the boundary conditions, (i) ux(0, t) ux(,0, andiii) u(r, 0)-P(), where P(x)-[1-cos (2 )6 + 20 cos(их) + 20 (Note the 6th power in the first term) Plot the solution, u(x,t), as a function of x at five curves in a single plot 0, 0.005, 0.03, 0.1, and 0.3. Please collect all (i) We expect the solution to be expressed as an infinite series. A truncation of the infinite series is needed to numerically compute the series in order to plot the solution. It is your job to determine the appropriate number of terms to keep. As a useful measure, the solution at t = 0 should match the given initial state in the 3rd boundary condition. If they do not match, either the solution is wrong or more terms need to be retained in the series. This remark applies to all future homework problems that require the evaluation of an infinite series. (ii) For the evaluation of the expansion coefficients in the infinite series, there is no need to carry out the integrations analytically. (If you wish to do so, please feel free to use an online integrator or similar software such as Wolfram Alpha. No need to do it by hand.) It is perfectly acceptable (actually, recommended for this problem) to evaluate the integrals numerically using Matlab or its equivalent. See additional note in the last page for an example of using Matlab to numerically evaluate an integral

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