Abstract: In this research article, we connect the \(K^{*}\) iterative process with the class of mappings having property (CSC). We provide some weak and strong convergence theorems regarding the iterative scheme for mappings endowed with property (CSC) in uniformly convex Banach spaces. An example of mappings endowed with property (CSC) is provided which does not satisfy property (C). The \(K^{*}\) iteration process and many other iterative processes are connected with this example to support the theoretical outcome. Our results improve and extend the corresponding well-known results of the current literature. PubDate: 2021-04-27

Abstract: In this manuscript, we investigate the approximate solutions to the tangent nonlinear packaging equation in the context of fractional calculus. It is an important equation because shock and vibrations are unavoidable circumstances for the packaged goods during transport from production plants to the consumer. We consider the fractal fractional Caputo operator and Atangana–Baleanu fractal fractional operator with nonsingular kernel to obtain the numerical consequences. Both fractal fractional techniques are equally good, but the Atangana–Baleanu Caputo method has an edge over Caputo method. For illustrations and clarity of our main results, we provided the numerical simulations of the approximate solutions and their physical interpretations. This paper contributes to the new applications of fractional calculus in packaging systems. PubDate: 2021-04-27

Abstract: Finite element methods have been frequently employed in seeking the numerical solutions of PDEs. In this study, a Galerkin finite element numerical scheme is constructed to explore numerical solutions of the generalized Kuramoto–Sivashinsky (gKS) equation. A quartic trigonometric tension (QTT) B-spline function is adapted as base of the Galerkin technique. The incorporation of B-spline Galerkin in space discretization generates the time-dependent system. Then, the use of Crank–Nicolson time integration algorithm to this system gives the wholly discretized scheme. The efficiency of the method is tested over several initial boundary value problems. In addition, the stability of the computational scheme is analyzed by considering Von Neumann technique. The computational results obtained by the suggested scheme are simulated and compared with the commonly existing numerical findings. PubDate: 2021-04-23

Abstract: Gegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their \(L^2\) -norm. PubDate: 2021-04-21

Abstract: In recent times, operational matrix methods become overmuch popular. Actually, we have many more operational matrix methods. In this study, a new remodeled method is offered to solve linear Fredholm–Volterra integro-differential equations (FVIDEs) with piecewise intervals using Chebyshev operational matrix method. Using the properties of the Chebyshev polynomials, the Chebyshev operational matrix method is used to reduce FVIDEs into a linear algebraic equations. Some numerical examples are solved to show the accuracy and validity of the proposed method. Moreover, the numerical results are compared with some numerical algorithm. PubDate: 2021-04-19

Abstract: A supporting vector of a matrix A for a certain norm \(\Vert \cdot \Vert \) on \(\mathbb {R}^n\) is a vector x such that \(\Vert x\Vert =1\) and \(\Vert Ax\Vert =\Vert A\Vert =\displaystyle \max _{\Vert y\Vert =1}\Vert Ay\Vert \) . In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the \(\ell _1\) -norm and the \(\ell _{\infty }\) -norm. Besides this characterization, our theorems provide a description of the set of supporting vectors for operators on \(\ell _{\infty }\) and \(\ell _1\) . As an application of our results in the finite-dimensional case for both the \(\ell _1\) -norm and the \(\ell _{\infty }\) -norm, we study meteorological data from stations located on the province of Cádiz (Spain). For it, we consider a matrix database with the highest temperature deviations of these stations. PubDate: 2021-04-18

Abstract: In this article, the numerical solution of glioma, or glioblastomas, which is one of the most aggressive forms of cancer is considered. A heterogeneous nonlinear diffusion logistic density model is taken as the main focus. To obtain the numerical results, three different discretization techniques: Pseudospectral method (PSM) using Chebyshev–Gauss–Lobatto collocation points, method of lines (MoL), and cubic B-splines (cBS) are employed on the spatial domain, whereas 4th-order Runge–Kutta (RK4) is considered on the time domain. Adapting cBS and PSM discretization to the glioma model is studied at first in this study. In addition to the theoretical convergence results, detailed comparative computational results are presented. All these methods are compared in terms of their efficiencies in varying time step and mesh discretization not only to one another, but also with the methods given in the literature. PubDate: 2021-04-15

Abstract: In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\) -type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\) -type binomial fractional difference sequence space \((1 \le r < \infty )\) by employing the Hausdorff measure of non-compactness. PubDate: 2021-04-12

Abstract: The combination of Sinc quadrature method and double exponential transformation (DE) is a powerful tool to approximate the singular integrals, and radial basis functions (RBFs) are useful for the higher-dimensional space problem. In this study, we develop a numerical method base on Gaussian-RBF combined with QR-factorization of arising matrix and DE-quadrature Sinc method to approximate the solution of two-dimensional space-fractional diffusion equations. When the number of central nodes increases, the ill-conditioning of resultant matrix can be eliminated by using GRBF-QR method. Two numerical examples have been presented to test the efficiency and accuracy of the method. PubDate: 2021-04-11

Abstract: Some discrete distributions generated by stable densities (DGSDs) could be considered as models for describing phenomena arising in bioinformatics. Since probability mass and distribution functions are not in closed forms, simulation studies and real applications of these distributions have not been studied yet. To do this, we need to consider DGSDs as truncated, namely, truncated DGSDs (T-DGSDs). In this paper, some statistical properties of the T-DGSDs models are established. Based on the Monte Carlo method, limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, and Nelder–Mead optimization algorithms, we do a simulation to estimate biases, mean square errors, and maximum likelihood estimations for the unknown parameters of the T-DGSDs. Moreover, we fit these T-DGSDs models with some real data sets in bioinformatics and then compare them to some frequency distributions. PubDate: 2021-04-08

Abstract: This work shed light on the solvability of a nonlinear Volterra integral equation in the case where the kernel of this equation is weakly singular. We certainly aim to get a precise solution. This can be achieved by applying a product integration method which is able to construct a nonlinear system. To solve the resulting system, it suffices to employ Broyden’s method. In the sequel, we add a computational application after the convergence proof of our approximate solution PubDate: 2021-04-08

Abstract: The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs. PubDate: 2021-03-30

Abstract: This paper provides a new three-parameter lifetime distribution with increasing and decreasing hazard function. The various statistical properties of the proposed distribution are also discussed. The maximum likelihood method is used for estimating the unknown parameters, and its performance is assessed using Monte-Carlo simulation. Finally, three real data sets are applied to illustrate the application of the proposed distribution. PubDate: 2021-03-29

Abstract: The present paper focuses on the improving split-step forward methods to solve of stiff stochastic differential equations of Itô type. These methods are based on the exponential modified Euler schemes. We show the convergency of our suggested explicit methods to solution of the corresponding stochastic differential equations in strong sense. For a test equation, mean-square stability of schemes are investigated. The numerical examples will be presented to support theoretical findings. PubDate: 2021-03-28

Abstract: In this note for every \(S\) -metric space \((X,S),\) we define a new \(S\) -metric \({S}_{H}\) called Hausdorff S-metric on \(CB(X)\) and show that if \((X,S)\) is complete, \((K\left(X\right), {S}_{H})\) is complete too, where K(X) is the set of all compact nonempty subsets of \(X\) and the notion of weak contraction multi-valued mappings on complete metric spaces (Kritsana Neammanee & Annop Kaewkhao, 2011) is generalized to complete \(S\) -metric spaces. This idea is used to establish some fixed-point theorems for weak contractive multi-valued mappings from \((X,S)\) into \((CB\left(X\right),{S}_{H})\) . PubDate: 2021-03-19

Abstract: In this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness of a positive solution and the Hyers–Ulam-type stability. To proceed this work, we utilize the tools of fixed point theory and nonlinear analysis to investigate the concern theory. We convert fractional differential equation into an integral alternative form with the help of the Greens function. Using the desired function, we studied the existence of a positive solution and uniqueness for proposed class of fractional differential equation. In next section of this work, the author presents stability analysis for considered problem and developed the conditions for Ulam’s type stabilities. Furthermore, we also provided two examples to illustrate our main work. PubDate: 2021-03-17

Abstract: This study proposes new statistical tools to analyze the counts of the daily coronavirus cases and deaths. Since the daily new deaths exhibit highly over-dispersion, we introduce a new two-parameter discrete distribution, called discrete generalized Lindley, which enables us to model all kinds of dispersion such as under-, equi-, and over-dispersion. Additionally, we introduce a new count regression model based on the proposed distribution to investigate the effects of the important risk factors on the counts of deaths for OECD countries. Three data sets are analyzed with proposed models and competitive models. Empirical findings show that air pollution, the proportion of obesity, and smokers in a population do not affect the counts of deaths for OECD countries. The interesting empirical result is that the countries with having higher alcohol consumption have lower counts of deaths. PubDate: 2021-03-16

Abstract: 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. PubDate: 2021-03-13

Abstract: In the present paper, we have established some fixed soft point results on soft S-metric and soft complete S-metric spaces. Instead of contraction or contractive soft mappings, we have considered two arbitrary soft mappings to prove the fixed-point results of soft complete S-metric spaces. We have also show that if the above two soft mappings are coincided, then these results are equivalent to the results formed by the other researchers. PubDate: 2021-03-08

Abstract: In this article, for the first time, a powerful numerical approach, named Sinc–Galerkin algorithm, is employed to explore the thermal performance of moving porous fin subject to nanoliquid flow. Different configurations of nanoparticle such as needle, sphere and disk shapes are considered here. The nonlinear differential equation is introduced and nondimensionalized. The presented governing equation is a nonlinear two-point boundary value problem which has been reduced to a system of nonlinear equations by means of Sinc–Galerkin approach. In order to deal with the ordinary differential equations, the vector matrix from is obtained and then the Newton iteration method is performed. The numerical results are graphically shown for different system parameters, and the impact of shaped nanoparticles on the enhancement of thermal behavior of porous fins is addressed and discussed. It is found that the nanoparticle with sphere configuration has the best influence on the rate of heat flux compared to other shaped nanoparticles. Moreover, it is revealed that the effect of wet porous parameter is to enhance the thermal features of permeable fins. PubDate: 2021-03-04