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Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula

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Abstract

An extension of the bivariate homogeneous orthogonal polynomials can be introduced by using a linear functional with complex moments obtained from the series expansions of a bivariate function at the origin and infinity. They are used to construct the bivariate homogeneous two-point Padé approximant and to solve related problems. In this paper we study the connection between extended homogeneous bivariate orthogonal polynomials and symbolic Gaussian cubature formula for the approximation of bivariate integrals over domains with non-negative weight functions. By extension to the two-point case, a new symbolic Gaussian cubature is presented. A new numerical cubature is also developed. Finally, some numerical examples are given to illustrate our results.

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Acknowledgements

The authors would like to thank the referees for their pertinent remarks and suggestions.

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Author notes

  1. Jilali Abouir and Brahim Benouahmane contributed equally to this work.

Authors and Affiliations

  1. Faculty of Sciences and Technology, Laboratory LMCMAN, University Hassan II of Casablanca, BP 146, Mohammedia, 20650, Morocco

    Jilali Abouir & Brahim Benouahmane

Authors
  1. Jilali Abouir
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  2. Brahim Benouahmane
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Contributions

The authors confirm contribution to the paper as follows: study conception: J.A., B.B.; analysis and interpretation of results: J.A., B.B.; draft manuscript preparation: J.A., B.B.; the authors reviewed the results and approved the final version of the manuscript.

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Correspondence to Jilali Abouir.

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Abouir, J., Benouahmane, B. Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula. Numer Algor 97, 1535–1561 (2024). https://doi.org/10.1007/s11075-024-01761-8

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  • DOI: https://doi.org/10.1007/s11075-024-01761-8

Keywords

Mathematics Subject Classification (2010)