A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Nonlinear integral equations solution method based on operational matrices of Chebyshev

2020
*
International Journal of Advanced and Applied Sciences
*

In this paper, the

doi:10.21833/ijaas.2020.05.013
fatcat:w4pqgbyiq5ar5mrfl5v43kgbhm
*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. ...##
###
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

2013
*
Zenodo
*

Then these properties are

doi:10.5281/zenodo.3470208
fatcat:ra3flw52ajbczhrdqwm76i3tvi
*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. ...##
###
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

2010
*
Journal of Guidance Control and Dynamics
*

Acknowledgments We gratefully acknowledge the generous funding provided by various agencies in support

doi:10.2514/1.45154
fatcat:fxau3vtv6nak3f3pznhrme3u5u
*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. ...##
###
Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

2018
*
Mathematical Problems in Engineering
*

Unsteady helicopter rotor flows are solved by a

doi:10.1155/2018/9745862
fatcat:3adpvbcqofhgfoqv6yydzcfpxm
*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. ...##
###
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

1975
*
Computers and Mathematics with Applications
*

This technique is

doi:10.1016/0898-1221(75)90018-8
fatcat:6vwyjt5wsjd3xhgcmxruiuk5ai
*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. ...##
###
Solution of Magnetohydrodynamic Flow in a Rectangular Duct by Chebyshev Polynomial Method

2012
*
Applied Mathematics
*

In present method,

doi:10.5923/j.am.20120203.03
fatcat:c4jpfdymz5ew7ivietg4vxiqti
*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 ...##
###
Moment LMI approach to LTV impulsive control

2013
*
52nd IEEE Conference on Decision and Control
*

Jointly with the

doi:10.1109/cdc.2013.6760805
dblp:conf/cdc/ClaeysAHL13
fatcat:yas2og5w5bejzb7qc2tvq3rg74
*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. ...##
###
Moment LMI approach to LTV impulsive control
[article]

2013
*
arXiv
*
pre-print

Jointly with the

arXiv:1303.1707v1
fatcat:c7vk62fr3rhkvkd2geqmp4tziu
*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. ...##
###
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

1997
*
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
*

We adapt concepts from the kernel

doi:10.1103/physreve.56.4822
fatcat:zorubzjrore2pnqoq24q2atjsa
*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. ...##
###
Wavelet Methods for Solving Fractional Order Differential Equations

2014
*
Mathematical Problems in Engineering
*

Fractional calculus is a field

doi:10.1155/2014/140453
fatcat:uhy5m3rorjbe7bezojqosg7o3m
*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. ...##
###
Master index to volumes 41–50

1994
*
Journal of Computational and Applied Mathematics
*

Vanmaele, Some results in lumped mass finite-element

doi:10.1016/0377-0427(94)90335-2
fatcat:hvkfefjn4bfqjhv6scsbkasrle
*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 ...
« Previous

*Showing results 1 — 15 out of 3,197 results*