Rational Laguerre Functions and Their Applications
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Authors
A. Aminataei
- Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
S. Ahmadi Asl
- Department of Mathematics, Birjand University, Birjand, Iran
Z. Kalatehbojdi
- Department of Mathematics, Birjand University, Birjand, Iran
Abstract
In this work, we introduce a new class of rational basis functions defined on \([a,b)\) and based on mapping
the Laguerre polynomials on the bounded domain \([a,b)\) . By using these rational functions as basic
functions, we implement spectral methods for numerical solutions of operator equations. Also the
quadrature formulae and operational matrices (derivative, integral and product) with respect to these basis
functions are obtained. We show that using quadrature formulae based on rational Laguerre functions give
us very good results for numerical integration of rational functions and also implementing spectral methods
based on these basis functions for solving stiff systems of ordinary differential equationsgive us suitable
results. The details of the convergence rates of these basis functions for the solutions of operator equations
are carried out, both theoretically and computationally and the error analysis is presented in \(L^2 [a,b)\)
space norm.
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ISRP Style
A. Aminataei, S. Ahmadi Asl, Z. Kalatehbojdi, Rational Laguerre Functions and Their Applications, Journal of Mathematics and Computer Science, 14 (2015), no. 2, 124-142
AMA Style
Aminataei A., Asl S. Ahmadi, Kalatehbojdi Z., Rational Laguerre Functions and Their Applications. J Math Comput SCI-JM. (2015); 14(2):124-142
Chicago/Turabian Style
Aminataei, A., Asl, S. Ahmadi, Kalatehbojdi, Z.. "Rational Laguerre Functions and Their Applications." Journal of Mathematics and Computer Science, 14, no. 2 (2015): 124-142
Keywords
- Rational Laguerre functions
- Spectral methods
- Quadrature formulae
- Stiff system
- Hilbert space.
MSC
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