فهرست مقالات Laguerre polynomial

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  1 - Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
  A. Riahifar M. Matinfar
  In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix o چکیده کامل

  In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds to a linear system of algebraic equations with unknown Laguerre coefficients‎. ‎We prove the convergence analysis of method applied to the solution integro-differential equations‎. ‎Finally‎, ‎numerical examples illustrate the efficiency and accuracy of the method. پرونده مقاله
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  2 - A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials
  P. Jami E. Hashemizadeh
  10.30495/ijim.2022.19201
  The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper w چکیده کامل

  The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method. پرونده مقاله
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  3 - The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear differential equations with variable coefficients
  Z Kalateh Bojdi S Ahmadi-Asl A Aminataei
  In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which e چکیده کامل

  In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierential equationsto solve a system of linear algebraic equations, thus greatly simplify the problem. In addition, severalnumerical experiments are given to demonstrate the validity and applicability of the method. پرونده مقاله
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  4 - Application of optimization algorithm to nonlinear fractional optimal control problems
  Asma Moradikashkooli Hamid Haj Seyyed Javadi Sam Jabbehdari
  10.22094/jcr.2023.1996770.1317
  In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivati چکیده کامل

  In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivatives of GLPs is constructed. The operational matrices of the Caputo and ordinary derivatives are introduced. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method. پرونده مقاله
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  5 - Numerical solution of Fredholm integral-differential equations on unbounded domain
  M. Matinfar A. Riahifar
  In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(G چکیده کامل

  In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution ofa system of linear algebraic equations with unknown generalized Laguerre coefficients. Inaddition, two examples are given to demonstrate the validity, efficiency and applicability ofthe technique. پرونده مقاله
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  6 - On Extension of Generalized Laguerre Polynomials of Two Variable
  Ahmed Al-Gonah
  In this paper, we introduce a new extension of generalized Laguerre polynomials of two variable by using the extended Beta function. Some properties of these extension polynomials such as generating functions, integral representation, recurrencerelations and summation f چکیده کامل

  In this paper, we introduce a new extension of generalized Laguerre polynomials of two variable by using the extended Beta function. Some properties of these extension polynomials such as generating functions, integral representation, recurrencerelations and summation formulae are obtained. پرونده مقاله
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  7 - A STRONG COMPUTATIONAL METHOD FOR SOLVING OF SYSTEM OF INFINITE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS
  M. Matinfar Abbas Riahifar H. Abdollahi
  The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coeffi چکیده کامل

  The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustrate the simplicity and the effectiveness of the proposed method have been presented. پرونده مقاله