Applications of orthogonal polynomials

Authors:
Maitree Podisuk;Witchaya Rattanametawee;Decha Samana
Affiliations:
Department of Mathematics and Computer Science, King Mongkut's Institute of Technology Chaokhuntaharn Ladkrabang, Ladkrabang, Bangkok, Thailand;Department of Mathematics and Computer Science, King Mongkut's Institute of Technology Chaokhuntaharn Ladkrabang, Ladkrabang, Bangkok, Thailand;Department of Mathematics and Computer Science, King Mongkut's Institute of Technology Chaokhuntaharn Ladkrabang, Ladkrabang, Bangkok, Thailand
Venue:
MATH'05 Proceedings of the 7th WSEAS International Conference on Applied Mathematics
Year:
2005

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Abstract

Orthogonal polynomials appear frequently in applied mathematics. In this paper, we will introduce two sequences of orthogonal polynomials on the interval [0,1]. The orthogonal polynomials of each type up to degree seven will be illustrated. We will use these fourteen orthogonal polynomials to obtain fourteen Gaussian quadrature formulas and fourteen formulas of Runge-Kutta type for solving the initial value problem of ordinary differential equation. Some examples will be given.