摘要:

A method is given for the approximation of generalized orthogonal polynomials (GOP) to solve the problems of fractional and operational calculus. A more rigorous derivation for the generalized orthogonal polynomial operational matrices is proposed. The Riemann-Liouville fractional integral for repeated fractional (and operational) integration is integrated exactly, then expanded in generalized orthogonal polynomials to yield the generalized orthogonal polynomial operational matrices. The generalized orthogonal polynomial operational matrices perform as sα(α ≥ αϵ R) in the Laplace domain and as fractional (and operational) integrators in the time domain. Using these results, inversions of the Laplace transforms of irrational and rational transfer functions are solved in a simple way. Very accurate results are obtained.

ISSN:0020-7721    

DOI:10.1080/00207728708964020

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The procedure for composing the spline function of order m that interpolates n data is roughly divided into two stages: (1) constructing the matrix Anthat transforms the fl-spline coefficient vector c into the sample value vector s; and (2) calculating the vector c. Then the effects of boundary conditions and the locations of the sampling points and the knots on the number of computations for spline interpolation are evaluated. There are no boundary condition effects of the construction of A" for equispacing. Non-periodic boundary conditions reduce the number of computations needed to calculate c from O(m2n) to O(m2n/4).

ISSN:0020-7721    

DOI:10.1080/00207728708964021

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The first part of this paper calculates the error between a function and its m-term Chebyshev series expansion. The second part calculates the error between the integral of a function and its m-term Chebyshev series obtained using the usual operational matrix of integration. The final part derives the error between the exact solution of a state equation and the m-term Chebyshev series solution obtained by the Chebyshev polynomial method.

ISSN:0020-7721    

DOI:10.1080/00207728708964022

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The convergence of the block-pulse series expansion of a function f(x, y) and its integral with respect to x and y is proved first. Then the convergence of the block-pulse series solution of a distributed parameter system obtained by the block-pulse series expansion method is proved.

ISSN:0020-7721    

DOI:10.1080/00207728708964023

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The Taylor series is introduced to analyse and approximate the solution of a class of scaled systems. Using the operational matrix of integration, together with the derived scaled operational matrix, the dynamical equation of a scaled system is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of the Taylor series expansion can be determined recursively by the derived algorithm. The parameter identification problems of scaled systems are also investigated. Owing to the simplicity of the operational matrix of integration and the scaled operational matrix, the Taylor series presents considerable computational advantages when compared with the other possible polynomial series, provided that both the input and output signals are analytic functions oft.

ISSN:0020-7721    

DOI:10.1080/00207728708964024

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Consider a G/M/K/O queueing loss system with K heterogeneous servers, exponentially distributed service times, no waiting room, a stationary counting arrival process, and an ordered entry. The ordered entry rule implies that, if the servers are indexed from 1 to K, units first arrive at the first server, then at the second server, and finally at theKth server. In this queueing system, units that find the servers busy are not lost. Those units re-try to receive service by merging with the incoming units to be reconsidered for service by one of the free servers. This queueing system is analysed in terms of approximating the flows of units inside the system by a two parameter method. An example is introduced and approximation results are compared with those from a simulation study.

ISSN:0020-7721    

DOI:10.1080/00207728708964025

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

A linear delay differential system of the form ẋ(t) = Ax(t — h), x(t) ε Rnis considered and simple analytic necessary and sufficient conditions for asymptotic stability are derived. The criterion is given in terms of the eigenvalues of the matrix A and the time delay h.

ISSN:0020-7721    

DOI:10.1080/00207728708964026

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor