Wang [26] studied the Fisher equation on a semi-infinite domain using the generalized
Laguerre functions. Wang and Jiao [27] considered the Fisher equation on unbounded domain using the generalized Hermite functions.
In particular, the polyBergman spaces are spaces of Wavelet transform which is related to
Laguerre functions, and the poly-Fock spaces are spaces of short-time Fourier transform which is related to Hermite functions.
A PRODUCT PROPERTY FOR DISCRETE TIME
LAGUERRE FUNCTIONS. PHILIP OLIVIER, UNIVERSITY OF SOUTH ALABAMA.
The method of approximation analyzed in this paper is the Laguerre Impulse Response Approximation (LIRA) which is based on approximation of noninteger order system impulse response with
Laguerre functions. Early works in this area were unsuccessful in approximation of [alpha] order integrators [18, 19].
There are two parameters in this model: the number of Laguerre orthogonal functions K and the pole of
Laguerre functions [lambda]([absolute value of [lambda]] < 1).
Very good results for such problems have been achieved by using nonclassical orthogonal basis sets for systems [9], mapped orthogonal systems [16,17],
Laguerre functions [10], mapped Legendre functions [11], and mapped Fourier sine series [12].
Different approaches have been considered for reducing the online computation time by discusses the Optimal Model Predictive Control (OMPC) which gives stability and recursive feasibility guarantee and is often assumed in modern MPC approaches.MPC implementation based on
Laguerre functions also called Laguerre optimal model predictive control (LOMPC) has been discussed in [11,12] enables the capture of near optimal control trajectory with less number of parameters as compared with conventional MPC algorithms.
The Rao-Wilton-Glisson (RWG) [26] functions are used as the spatial expansion and testing functions, and the weighted
Laguerre functions are used as the temporal expansion and testing functions.
In this paper, we propose an efficient and accurate method to apply FDTD for transient wave propagation in a general dispersive media using the MOD scheme with the associate
Laguerre functions. This MOD methodology has been successfully implemented in a FDTD formulation [10-14] and in integral equations dealing with skin effects in conductors, and propagation in non-dispersive dielectric and in a dispersive media [15-17].
The most important special functions are known as: Bessel functions, Hermite functions, Legendre functions,
Laguerre functions, Chebyshev functions etc., [10].
Lindsay, and V Pavlov, (2005), 'Smooth estimation of yield curves by
Laguerre functions', In: MODSIM 05--International Congress on Modelling and Simulation Advances and Applications for Management and Decision Making, 12 December-15 December, 2005, Australia, Victoria, Melbourne.
