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Nonlinear integral equations solution method based on operational matrices of Chebyshev

Jumah Aswad Zarnan, Department of Accounting by IT, Cihan University, Sulaimaniya, Kurdistan, Iraq
2020 International Journal of Advanced and Applied Sciences  
In this paper, the solution of Hammerstein integral equations is presented by a new approximation method based on operational matrices of Chebyshev polynomials.  ...  The nonlinear Hammerstein and Volterra Hammerstein integral equations are reduced to a system of nonlinear algebraic equations by using operational matrices of Chebyshev polynomials.  ...  Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest.  ... 
doi:10.21833/ijaas.2020.05.013 fatcat:w4pqgbyiq5ar5mrfl5v43kgbhm

Page 2100 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
The singular behavior of the unknown function is explicitly built into the solution using the index theorem. The integral equation is replaced by integral relations at a discrete set of points.  ...  It may be added that the solutions of these dual equations are determined in terms of an unknown function g(t) which happens to satisfy a Fredholm equation of the third kind.”  ... 

Solving Fredholm Integral Equations with Bernstein Multi-Scaling Functions

S Davaei far, Yadollah Ordokhani
2013 Zenodo  
Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation which is compatible to an algebraic equations system.  ...  In this article, efficient numerical methods for finding solution of linear and nonlinear Fredholm integral equations of the second kind based on Bernstein multi scaling functions are presented.  ...  Acknowledgments Authors are very grateful to refers for reading the paper carefully and for comments and suggestions which improved the quality of paper.  ... 
doi:10.5281/zenodo.3470208 fatcat:ra3flw52ajbczhrdqwm76i3tvi

Page 6607 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
Summary: “In this paper, the Chebyshev matrix method is ap- plied to generalisations of the Hermite, Laguerre, Legendre and Chebyshev differential equations which have polynomial solutions.  ...  A method is pre- sented which uses polynomial splines to approximate the solutions of the system. Error estimates, stability properties and conver- gence of the method are discussed.  ... 

Costate Computation by a Chebyshev Pseudospectral Method

Qi Gong, I. Michael Ross, Friba Fahroo
2010 Journal of Guidance Control and Dynamics  
Acknowledgments We gratefully acknowledge the generous funding provided by various agencies in support of this research. The research of Q. Gong  ...  Using D as an adjoint Chebyshev differentiation matrix, we define the primal-dual PS discretization of Problem B as follows.  ...  Fig. 3 3 Primal-feasible solutions as candidate optimal solutions. Fig. 4 4 Dual feasible solution by the Chebyshev PS method. Fig. 5 5 Verification of Hamiltonian minimization condition.  ... 
doi:10.2514/1.45154 fatcat:fxau3vtv6nak3f3pznhrme3u5u

Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

Dong Kyun Im, Seongim Choi
2018 Mathematical Problems in Engineering  
Unsteady helicopter rotor flows are solved by a Chebyshev pseudospectral method with overset mesh topology which employs Chebyshev polynomials for solution approximation and a Chebyshev collocation operator  ...  to represent the time derivative term of the unsteady flow governing equations.  ...  Acknowledgments This work was supported by Youngsan University Research Fund of 2018.  ... 
doi:10.1155/2018/9745862 fatcat:3adpvbcqofhgfoqv6yydzcfpxm

Page 4076 of Mathematical Reviews Vol. , Issue 86i [page]

1986 Mathematical Reviews  
Then he gives the solution of the latter system for some classes of 1-kernels by the method of successive approximations.  ...  I. 86i:45015 Some unbiased estimates of solutions of equations with polynomial nonlinearity. (Russian. English summary) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1985, vyp. 1, 107-109, 123.  ... 

An algorithm for solving a dual cosine series

Robert B. Kelman, J. Timothy Simpson
1975 Computers and Mathematics with Applications  
This technique is used to reduce to an algorithm the analytic solution to a dual cosine series which had earlier been derived by the method of orthogonality relations.  ...  Solutions to dual trigonometric series arefrequently given as double singular integrals, which are not conducive to automatic numerical evaluation.  ...  Let us expand p', in Legendre polynomials and use the integral representation [25, p. 786] T,(y)-T,+,(y) = (i +!)y(ly) f yf;(~)y) dx where T, is the Chebyshev polynomial of the first kind.  ... 
doi:10.1016/0898-1221(75)90018-8 fatcat:6vwyjt5wsjd3xhgcmxruiuk5ai

Solution of Magnetohydrodynamic Flow in a Rectangular Duct by Chebyshev Polynomial Method

İbrahim Çelik
2012 Applied Mathematics  
In present method, approximate solution is taken as truncated Chebyshev series.  ...  In this study, Chebyshev polynomial method is applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field.  ...  The aim of this paper is to use Chebyshev Polynomial Method for which approximate solution is taken as truncated Chebyshev series towards obtaining velocity and induced magnetic field for the steady-state  ... 
doi:10.5923/j.am.20120203.03 fatcat:c4jpfdymz5ew7ivietg4vxiqti

Moment LMI approach to LTV impulsive control

Mathieu Claeys, Denis Arzelier, Didier Henrion, Jean-Bernard Lasserre
2013 52nd IEEE Conference on Decision and Control  
Jointly with the use of Chebyshev polynomials (as a numerically more stable polynomial basis), this allows LMI relaxations of high order (up to a few hundreds) to be solved numerically.  ...  Linearity of the dynamics allows us to integrate system trajectories and to come up with a simplified LMI hierarchy where the only unknowns are moments of a vector of control measures of time.  ...  These data are calculated by numerical integration, using Chebyshev polynomial approximations, as explained in the last section.  ... 
doi:10.1109/cdc.2013.6760805 dblp:conf/cdc/ClaeysAHL13 fatcat:yas2og5w5bejzb7qc2tvq3rg74

Moment LMI approach to LTV impulsive control [article]

Mathieu Claeys, Didier Henrion (LAAS, CTU/FEE), Jean-Bernard Bernard Lasserre
2013 arXiv   pre-print
Jointly with the use of Chebyshev polynomials (as a numerically more stable polynomial basis), this allows LMI relaxations of high order (up to a few hundreds) to be solved numerically.  ...  Linearity of the dynamics allows us to integrate system trajectories and to come up with a simplified LMI hierarchy where the only unknowns are moments of a vector of control measures of time.  ...  These data are calculated by numerical integration, using Chebyshev polynomial approximations, as explained in the last section.  ... 
arXiv:1303.1707v1 fatcat:c7vk62fr3rhkvkd2geqmp4tziu

Page 226 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
It uses polynomial expansion to approximate ‘¥/w on each analytic area, where w is a Chebyshev weight function, with a basis of Chebyshev polynomials.  ...  The authors study conformal maps via the solution of Symm’s integral equation f,. ‘¥(x) log|z — x||dx| = g(z). The Chebyshev collocation method is used for solving this equation.  ... 

Calculation of densities of states and spectral functions by Chebyshev recursion and maximum entropy

R. N. Silver, H. Röder
1997 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We adapt concepts from the kernel polynomial approximation, a linear Chebyshev approximation with optimized Gibbs damping, to control the accuracy of Fourier integrals of positive non-analytic functions  ...  We compare the performance of kernel polynomial and maximum entropy algorithms for an electronic structure example.  ...  Department of Energy. We thank D. Drabold, J. J. Dong for kind permission to use the example reported here. We thank D. Drabold and J. Kress for helpful comments on the manuscript.  ... 
doi:10.1103/physreve.56.4822 fatcat:zorubzjrore2pnqoq24q2atjsa

Wavelet Methods for Solving Fractional Order Differential Equations

A. K. Gupta, S. Saha Ray
2014 Mathematical Problems in Engineering  
Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders.  ...  We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/140453 fatcat:uhy5m3rorjbe7bezojqosg7o3m

Master index to volumes 41–50

1994 Journal of Computational and Applied Mathematics  
Vanmaele, Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas Andres, J., Asymptotic properties of solutions to quasi-linear differential  ...  Petzold, Projected collocation for higherorder higher-index differential-algebraic equations Askey, R., Problems which interest and/or annoy me Atanassova, L., On the simultaneous determination of the  ...  Masani, P.R., The measure-theoretic aspects of entropy, Part II Mason, J.C., Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms  ... 
doi:10.1016/0377-0427(94)90335-2 fatcat:hvkfefjn4bfqjhv6scsbkasrle
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