## Abstract

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.

## Authors

**Călin-Ioan Gheorghiu **

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

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

soon

## Cite this paper as:

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

## About this paper

##### Journal

AIP Publishing Conference Proceedings

##### Publisher Name

AIP Publishing

##### Print ISSN

Not available yet.

##### Online ISSN

Not available yet.

##### Google Scholar Profile

soon

## References

[1] D. Bonheure, J. M. Gomes and L. Sanchez, Nonlinear Analysis 61, 1383–1399 (2005).

[2] W. Gautschi, Orthogonal Polynomials in MATLAB. Exercises and Solutions, SIAM Philadeplphia, 2016.

[3] C.I. Gheorghiu, Numer. Algor. 68, 1–14 (2015).

[4] C.I. Gheorghiu, *Spectral Collocation Solutions to Problems on Unbounded Domains*, Casa Cărții de Stiință Publishing House, Cluj-Napoca, 2018.

[5] G. Kitzhofer, O. Koch, P. Lima and E. Weinmüller, J. Sci. Comput. 32, 411–424 (2007).

[6] P.M. Lima, N.B. Konyukhov, A.I. Sukov and N.V. Chemetov, J. Comput. Appl. Math. 189, 260–273 (2006).

[7] J.A.C. Weideman, International Series of Numerical Mathematics 131, 239–251 (1999).