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Generate the appropriate matrix - vector system to solve on the interval using discretization points. This requires you to define and load the matrix accordingly.
Generate the appropriate matrixvector system to solve
on the interval
using
discretization points. This requires you to define
and load the matrix accordingly.
Test the method for solving this problem using the true solution
This means
Include plots of the approximate versus the true solution in your submission. Save as png or jpg files. Provide a picture to the discussion forum.
Solve the system using
and
discretization points. Calculate the error and note the convergence rate. To compute the error, use
errorValsi normsinpixvals uapprox, inf
where uapprox is the solution obtained after solving the matrixvector system. Several codes loaded to Canvas MATLAB Codes Module will be useful here: uDoublePrime.m Download uDoublePrime.m uDoublePrimeSP.m Download uDoublePrimeSP.m and boundaryProbConv.m Download boundaryProbConv.m
Use both uDoublePrimeSP.m and uDoublePrime.m to generate the matrices for this problem. Note any differences between the two methods used to generate the matrices, especially with regards to solution times and ability to store the matrices.
Summarize your work in a document and upload to Canvas. Do not forget to include supporting code.
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