Solving Ax=b with both unknowns in A and b

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Hai Nguyen 2019-8-13

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https://ww2.mathworks.cn/matlabcentral/answers/475926-solving-ax-b-with-both-unknowns-in-a-and-b

评论： Torsten 2019-8-15

Anyone please help me with this problem. I only know some basic when it comes to matlab and having lots of difficulties trying to code this matrix problem Ax=b that have unknown in both A and b.

The linear system obtained in the form of

where

are constants, m is time step,

(initial and boundary values - W at t=0 and W at the last node and outside =0)

How to create the tridiagonal matrix A and vector b in matalb please? I tried to search similiar codes but only found the equations where A and b are known...in this case A and b have symbolic arguments in power form and they are related to the solution

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Walter Roberson 2019-8-13

diag(vector1, -1) + diag(vector2) + diag(vector3, 1)

builds a tridiagonal matrix.

Walter Roberson 2019-8-13

All of the j=i-1 entries are constructed the same way and they all fall along the diagonal just to the left of the major diagonal

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Torsten 2019-8-13

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编辑：Torsten 2019-8-13

Now if W_{0}^{m} and W_{N+1}^{m} are 0 (I think you meant W_{0}^{m} instead of W_{N}^{m}), you have a system of N equations in W_{1}^{m},...,W_{N}^{m}.

You can use Walter's suggestion to solve for W_{1}^{m+1},...,W_{N}^{m+1}.

I don't understand why you write that there are unknowns in A and b. The W's in A and b are the W's from the last time step (m) and thus known. The unkowns are W_{1}^{m+1},...,W_{N}^{m+1}.

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Hai Nguyen 2019-8-15

Thank you Sir for your kindness and patience. If I would like to reduce the time step from 1 to 0.01, which lines of the above program I need to change?