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Chebyshev polynomials and continued fractions related

Szczepański Jerzy

Science, Technology and Innovation

2019

Vol. 7, no. 4

1--8

Let p, q be complex polynomials, deg p>deg q ≥ 0. We consider the family of polynomials defined by the recurrence P_{n+1}=2pP_n-qP_{n-1) for n=1, 2, 3, ... with arbitrary P_1 and P_0 as well as the domain of the convergence of the infinite continued fraction f(z)=2p(z)-\cfrac{q(z)}{2p(z)-\cfrac{q(z)}{2p(z)-...

Realization of uniform approximation by applying mean-square approximation

Purczyński J.

Computer Applications in Electrical Engineering

2013

Vol. 11

34--45

In the paper the polynomial mean-square approximation method was applied, where the applied criterion was the value of the maximum error of the obtained approximation. The value of this error depends on the number of approximation points within the range. By changing the number of points within the range, it can be noticed that the value of the maximum error has the minimum value for a particular value of L number of considered points. For a polynomial of N degree, the optimum number of equidistant points of approximation L and the maximum error of approximation are determined. The proposed method was compared with a uniform approximation method, namely the Chebyshev polynomial. The examples included in the paper show that the proposed method yields smaller values of the maximum error than Chebyshev polynomial.

Nonlinear static and dynamic analysis of functionally graded plates

Wu T. L., Shukla K. K., Huang J. H.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 3

679-698

Explicit solution for the nonlinear static and dynamic responses of the functionally graded materials rectangular plate is obtained. The volume fraction of the material constituents is assumed to follow a simple power law distribution. The formulation is based on the first-order shear deformation theory and von-Karman nonlinear kinematics. Solution methodology utilizes quadratic extrapolation technique for linearization, finite double Chebyshev series for spatial discretization of the variables and Houbolt time marching scheme for temporal discretization. Numerical results show the effect of volume fraction exponent of the constituent materials on the nonlinear static and dynamic responses of the plate with different boundary conditions and plate span to thickness ratio. Analysis results indicate that the effect of the volume fraction exponent n up to two on the displacement of the plate is more significant.