Using the backward Euler and upwinding to solve the viscous Burgers equation

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Mat Hunt
Mat Hunt 2023-7-14
评论： Mat Hunt 2023-7-14
I wish to solve the following partial differential equation:
I have had some success using the backward Euler method for other linear equations and the upwinding approach. When I have tried it for the viscous burgers equation, it seems to have failed after the first step, and I have no idea why.
Can anyone point to where it seems to have gone wrong?

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采纳的回答

Mat Hunt
Mat Hunt 2023-7-14
This issue was the size of b, I reduced this and it worked perfectly. I find this odd as backward Euler is touted to be unconditionally convergent.

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Torsten
Torsten 2023-7-14
移动：Torsten 2023-7-14
Why don't you use ode15s to solve the semi-discretized system of ordinary differential equations ?
Look up "method-of-lines" for more details.
Or even better: "pdepe" is your friend.
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Torsten
Torsten 2023-7-14
编辑：Torsten 2023-7-14
Advanced integration methods make the solvers more sensitive, and they might give up even if continuing would still yield a good solution. But integrating without adaptive stepsize to control the error you make in the solution is no alternative in my opinion.
But I don't want to critisize your coding - I have the impression that you work responsibly :-)
Mat Hunt
Mat Hunt 2023-7-14
Coding up is not the problem, it's the numerical method that is the thing which is somewhat elusive.

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