1,720,975 research outputs found
Numerical treatment of fractional-order nonlinear system of delay integro-differential equations arising in biology
No full textThis paper presents a fractional-order nonlinear system of delay integro-differential equations which is used to model biological species living together. A numerical scheme based on the Chelyshkov polynomials is implemented to solve this fractional order system of integro-differential equations. The main advantages of the presented method is that it reduces under consideration problem to a system of nonlinear algebraic equations. Some test problems are considered to confirm validity and accuracy of the presented method. Moreover, the obtained numerical results are compared with those existing in the literature
A discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equations
No full textThis paper develops a numerical approach for solving coupled systems of nonlinear fractional order integro-differential equations(NFIDE). Shifted discrete Chebyshev polynomials (SDCPs) have been introduced and their attributes have been checked. Fractional operational matrices for the orthogonal polynomials are also acquired. A numerical algorithm supported by the discrete orthogonal polynomials and operational matrices are used to approximate solution of coupled systems of NFIDE. The operational matrices of fractional integration and product are applied for approximate the unknown functions directly. These approximations were put in the coupled systems of NFIDE. A comparison has been made between the absolute error of approximate solutions of SDCPs method with previous published. The gained numerical conclusions disclose that utilizing discrete Chebyshev polynomials are more efficient in comparison to the other methods
Frequency evaluation for adapted peer methods
No full textIn this paper, we consider exponentially fitted peer methods for the numerical solution of first order differential equations and we investigate how the frequencies can be tuned in order to obtain the maximal benefit. We will show that the key is analyzing the error's behavior. Formulae for optimal frequencies are computed. Numerical experiments show the properties of the proposed algorithm
A Comparative Approach for Time-Delay Fractional Optimal Control Problems: Discrete Versus Continuous Chebyshev Polynomials
No full textThis paper aims to demonstrate the superiority of the discrete Chebyshev polynomials over the classical Chebyshev polynomials for solving time-delay fractional optimal control problems (TDFOCPs). The discrete Chebyshev polynomials have been introduced and their properties are investigated thoroughly. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by these polynomials with unknown coefficients. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algabric system. A comparison has been made between the required CPU time and accuracy of the discrete and continuous Chebyshev polynomials methods. The obtained numerical results reveal that utilizing discrete Chebyshev polynomials is more efficient and less time-consuming in comparison to the continuous Chebyshev polynomials
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems
No full textIn this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann–Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs
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