Spectral collocation based on quasi-classical orthogonal polynomials applied to solve a singular BVP from Hydrodynamics

It is well established that spectral collocation methods based on classical orthogonal polynomials, in spite of their high order accuracy, use bad conditioned differentiation matrices, i.e., fully populated, rather non-normal and badly conditioned with respect to inversion.

The aim of this essay is to try to find other orthogonal polynomials, with respect to more sophisticated measures, which could generate better differentiation matrices and consequently more accurate collocation methods. We are mainly interested in solving boundary value problems on unbounded intervals.

Călin-Ioan Gheorghiu 
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

spectral collocation; orthogonal polynomial; non standard; sinc function; boundary value problem; unbounded domain

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C.I. Gheorghiu, Spectral collocation based on quasi-classical orthogonal polynomials applied to solve a singular BVP from Hydrodynamics, AIP Conference Proceedings 2293, 100004 (2020), DOI: 10.1063/5.0026783

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