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The purpose of this paper is to develop a new method based on operational matrices of two-dimensional delta functions for solving two-dimensional nonlinear quadratic integral equations (2D-QIEs) of fractional order, numerically.

For this aim, two-dimensional delta functions are introduced, and their properties are expressed. Then, the fractional operational matrix of integration based on two-dimensional delta functions is calculated for the first time.

By applying the operational matrices, the main problem would be transformed into a nonlinear system of algebraic equations which can be solved by using Newton's iterative method. Also, a few results related to error estimate and convergence analysis of the proposed method are investigated.

Two numerical examples are presented to show the validity and applicability of the suggested approach. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.

By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.

Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

The purpose of this paper is to develop a block method of order five for the general solution of the first-order initial value problems for Volterra integro-differential equations (VIDEs).

A collocation approximation method is adopted using the shifted Legendre polynomial as the basis function, and the developed method is applied as simultaneous integrators on the first-order VIDEs.

The new block method possessed the desirable feature of the Runge–Kutta method of being self-starting, hence eliminating the use of predictors.

In this paper, some information about solving VIDEs is provided. The authors have presented and illustrated the collocation approximation method using the shifted Legendre polynomial as the basis function to investigate solving an initial value problem in the class of VIDEs, which are very difficult, if not impossible, to solve analytically. With the block approach, the non-self-starting nature associated with the predictor corrector method has been eliminated. Unlike the approach in the predictor corrector method where additional equations are supplied from a different formulation, all the additional equations are from the same continuous formulation which shows the beauty of the method. However, the absolute stability region showed that the method is A-stable, and the application of this method to practical problems revealed that the method is more accurate than earlier methods.

The purpose of this study was a longitudinal study on knowledge organization (KO) realm structure and cluster concepts and emerging KO events based on co-occurrence analysis.

This longitudinal study uses the co-occurrence analysis. This research population includes keywords of articles indexed in the Web of Science Core Collection 1975–1999 and 2000–2018. Hierarchical clustering, multidimensional scaling and co-occurrence analysis were used to conduct the present research. SPSS, UCINET, VOSviewer and NetDraw were used to analyze and visualize data.

The “Information Technology” in 1975–1999 and the “Information Literacy” in 2000–2018, with the highest frequency, were identified as the most widely used keywords of KO in the world. In the first period, the cluster “Knowledge Management” had the highest centrality, the cluster “Strategic Planning” had the highest density in 2000–2018 and the cluster “Information Retrieval” had the highest centrality and density. The two-dimensional map of KO’s thematic and clustering of KO topics by cluster analysis method indicates that in the periods examined in this study, thematic clusters had much overlap in terms of concept and content.

The present article uses a longitudinal study to examine the KO’s publications in the past half-century. This paper also uses hierarchical clustering and multidimensional scaling methods. Studying the concepts and thematic trends in KO can impact organizing information as the core of libraries, museums and archives. Also, it can scheme information organizing and promote knowledge management. Because the results obtained from this article can help KO policymakers determine and design the roadmap, research planning, and micro and macro budgeting processes.