Write the equation system that we get by evaluating equation (1) in all of the N cells on matrix form, i.e., write the equation as Au=b, where u is a vector with N elements. What does the matrix A and the vector b look like?
(1)
b. Write a Matlab code that solves the equation system for the specified boundary conditions and a given number of cells N. The tricky part is to generate the matrix A.
TIPS: Use the Matlab commands spdiags, sparse, inv, zeros, and ones. Use the sparse function to reduce the computational time.
c. Calculate the error (e) according to equation (2) for 10 different values of N spaning from N=10 to N=1000. The Matlab command logspace might be useful here. Make a plot that shows the error as a function of N. Use the command loglog instead of plot. How does the error decay as a function of N?
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