I am reading Lloyd N. Trefethen's book "Spectral Methods in Matlab". For the fixed wall condition u(±1)=u'(±1）=0 of the fourth order equation, he used p=(1-x ^ 2) q (x) to convert the fixed wall condition into the Dirichlet condition.Then use the Chebyshev collocation method to solve. I would like to ask what substitution should be made for p when u (± 1)=u '' (± 1)=0? Looking forward to your reply. Thank you for your patience
Anton E. KulaginThank you, I'll give it a try. If the boundary condition becomes u (-1)=u '(-1)=0, u (1)=u' '(1)=0, do you have any new ideas
Anton E. Kulagin Thank you for your reply. I calculated an example where u''''(x)=e ^ (x ^ 2), and the boundary condition is u (± 1)=u '' (± 1)=0. I set u (x)=(1-x ^ 2) ^ 2q (x), and required q (± 1)=0. The results are different from the ones I proposed using Weidman and Reddy to validate a MATALAB differential matrix suite. So I need to think again. Thank you for your reply.
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