A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.

A numerical scheme for the solution of neutral integro-differential equations including variable delay

In this study, an effective numerical technique has been introduced for finding the solutions of the first-order integro-differential equations including neutral terms with variable delays. The problem has been defined by using the neutral integro-differential equations with initial value. Then, an alternative numerical method has been introduced for solving these type of problems. The method is expressed by fundamental matrices, Laguerre polynomials with their matrix forms. Besides, the solution has been obtained by using the collocation points with regard to the reduced system of algebraic equations and Laguerre series.

On the Degree of Approximation of a Function by Nörlund Means of its Fourier Laguerre Series

In this paper, we have proved the degree of approximation of function belonging to L[0, ∞) by Nörlund Summability of Fourier-Laguerre series at the end point x = 0. The purpose of this paper is to concentrate on the approximation relations of the function in L[0, ∞) by Nörlund Summability of Fourier- Laguerre series associate with the given function motivated by the works [3], [9] and [13].

Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model

Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim sizes of sample. However, whether the estimators are asymptotically normal or not is unknown. In this paper, we give the details to verify the asymptotic normality of these estimators and present some simulation examples to support our result.

Analytical Approach to Estimating Total Migration Time of Virtual Machines With Various Applications

Cloud applications and services such as social networks, file sharing services, and file storage have become increasingly popular among users in recent years. This leads to the enlargement of data centers, and an increase in the number of servers and virtual machines. In such systems, live migration is used to move virtual machines from one server to another, which affects the quality of service. Therefore, the problem of finding the total migration time is relevant. This article proposes analytical approach to obtaining analytical expression of the probability density of the total migration time based on the use of the apparatus of characteristic functions. The obtained expression is used to calculate characteristics of migration, taking into account the applications contributing the most randomness to the total migration time. To simplify the calculation of migration characteristics, the use of the Laguerre series can be recommended as giving more reliable results compared to Gram-Charlier series.