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

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Mat Hunt 2023-7-14

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评论： Mat Hunt 2023-7-14

采纳的回答： Mat Hunt

viscous_burgers.m

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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Mat Hunt 2023-7-14

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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 2023-7-14

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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 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 2023-7-14