University of Abudhabi Engineering Matlab Parabolic Equation Paper

I’m working on a numerical analysis exercise and need support to help me understand better.

Need a help to Solve the following parabolic equation and find U(x, t): by hand writing and create your own MATLAB you can see the sample of coding in the next pages but don’t copy and paste it. write one conclusion paragraph about the steps and results . all should be as a report include tables and graphs and coding.

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Solve the following parabolic equation and find U(x, t):

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Under the following initial and boundary conditions:

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U(x, 0) =f(x)=

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U(0,t)=U(L,t)=0;

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Where

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Use Implicit method to solve this problem for step sizes of :

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Compare your numerical solutions using appropriate measures ( e.g. calculating the errors, and demonstrating the results in graphs and etc..)with the the results obtained through explicit discretization and the exact solution which is :

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( exact solution)