Overflow Issue with High-Order D-Matrix in Chebyshev Spectral Method

[shashank singh]

Dear Dedalus Experts and members

I am Shashank Singh from India.

I was attempting to solve the third order Korteweg–De Vries equation, using Chebyshev spectral method but was facing issue of overflow, but when I tried same thing with Burgers' equation it worked, so does for other second and first order PDEs.

But when I am switching to third or higher order with IMEX RK time stepping it blows up. Could someone please suggest an issue? I think the issue is associated with D-matrix, as the order of D-matrix will increase the values will get very high with time stepping and eventually blow up.

I would really appreciate if someone could please suggest me the solution to this problem.

Thank you, 

Regards,

Shashank Singh

[shashank singh]

Dear Dedalus experts and members,

I was attempting to solve third order Korteweg–De Vries equation, using Chebyshev spectral method but was facing issue of overflow, but when I tried same thing with Burgers' equation it worked, so does for other second and first order PDEs. But when I am switching to third or higher order with IMEX RK time stepping it blows up. 
Could anyone please suggest issue, I think the issue is associated with D-matrix, as the order of D-matrix will increase the values will get very high with time stepping and eventually blow up. I would really appreciate if someone could please suggest me the solution to this problem.

[Daniel Lecoanet]

Hi Shashank,

We have studied this problem in this paper:

Daniel

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