Multidomain and Preconditioning Schemes for Computing Higher Derivatives

A multidomain method and a preconditioning scheme are investigated for computing the Chebyshev spectral derivative. Error analysis shows that the proposed multidomain method , as the number of subdomain increases, numerical solution comes close to the exact solution. Other aspects of the multidomain method like CPU time, memory allocation and smalness of entries of differentiation matrix are also studied. Using Tal-Ezer mapping and the multidomain method the error in computing Chebyshev collocation derivative can be reduced. We have also used preconditioning to reduce the roundoff error in computing high order Chebyshev collocation derivative.

Chebyshev coolocation derivative; multidomain; differentiation matrix; Tal-Ezer mapping; Preconditioning