PDE system - pdepe system example - error or incomplete description on Matlab website?

2019 12 19
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更新时间：2019 12 24
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I am no longer sure how to use Matlab's pdepe properly for solving a system of PDEs after checking the example given on Matlab's help website.
If you look to an example here https://www.mathworks.com/help/matlab/math/solve-angio-pde-system.html under the 'Code Equation' you'll see a rewritten pde system in a matrix form. Comparing it to the original equation it is obvious that either the term " a*dndx*dcdx " is missing from the first (rewritten) equation, or Matlab implicity assumes that the derivative is acting only on the dudx terms when it deals with pde systems (this will be very weird). Could anyone with an extensive experiece in solving pde systems in Matlab clarify this?
Thanks

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Bill Greene
Bill Greene 2019-12-20

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Looks like you have found an error in this documentation page. If you look at equation 3 in the referenced paper you will see that this equation corresponds to what is actually coded in the pdepe example. The results from the pdepe analysis agree with figures 3 and 4 in the referenced paper. It is the first PDE in the documentation page that is incorrect.

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Leonid
Leonid 2019-12-23
Thanks for your answer. Based on the referenced paper it is the documentation page that contains error.
One additional thing that will be helpful to clarify:
If the coefficients d and a were functins of x [for example defined by some discrete data (and then interpolated within the function)], whould their derivatives through the flux term be taken into account by Matlab pdepe?

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