Authors:Naushad Mamode Khan; Vandna Jowaheer; Yuvraj Sunecher; Marcelo Bourguignon Abstract: This paper introduces an observation-driven (OD) longitudinal integer-valued moving average model of order 1 (INMA(1)) with COM–Poisson innovations under non-stationary moment conditions. This new longitudinal model provides lot of practical flexibility in terms of modeling a wide range of over-, under-dispersion and any mixed level of dispersion. In this set-up, the model parameters of primary interest consist of the regression and dispersion effects while the serial autocorrelation parameters are treated as nuisance. A robust Generalized Quasi-Likelihood approach is formulated to estimate the different set of parameters. The performance of the estimating algorithm is assessed via Monte Carlo experiments under various combination of the serial and dispersion values and is compared with the existing adaptive generalized method of moments. Application to two medical data: epileptic seizures and polyposis counts are also illustrated. PubDate: 2018-04-25 DOI: 10.1007/s40314-018-0621-7
Authors:Khaled M. Saad; Dumitru Baleanu; Abdon Atangana Abstract: In this paper, we extend the model of the Korteweg–de Vries (KDV) and Korteweg–de Vries–Burger’s (KDVB) to new model time fractional Korteweg–de Vries (TFKDV) and time fractional Korteweg–de Vries-Burger’s (TFKDVB) with Liouville–Caputo (LC), Caputo–Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville–Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB. PubDate: 2018-04-23 DOI: 10.1007/s40314-018-0627-1
Authors:Noureddine Benrabia; Hamza Guebbai Abstract: In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods. PubDate: 2018-04-23 DOI: 10.1007/s40314-018-0625-3
Authors:Hai-Long Shen; Peng-Fei Nie; Xin-Hui Shao; Chang-Jun Li Abstract: In this paper, we first propose a new Uzawa-SOR method for fourth-order block saddle point problems. Then we study its convergence conditions through some lemmas and theorems. Finally, the numerical results are presented to prove the 4-USOR method we proposed has less workload per iteration and higher accuracy for large linear system than the other Uzawa-type methods for solving the fourth-order block saddle point problem, which shows the effectiveness and feasibility of our method. PubDate: 2018-04-23 DOI: 10.1007/s40314-018-0623-5
Authors:D. Mathale; P. G. Dlamini; M. Khumalo Abstract: In this paper, we present a new application of higher order compact finite differences to solve nonlinear initial value problems exhibiting chaotic behaviour. The method involves dividing the domain of the problem into multiple sub-domains, with each sub-domain integrated using higher order compact finite difference schemes. The nonlinearity is dealt using a Gauss–Seidel-like relaxation. The method is, therefore, referred to as the multi-domain compact finite difference relaxation method (MD-CFDRM). In this new application, the MD-CFDRM is used to solve famous chaotic systems and hyperchaotic systems. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The results are compared with spectral-based multi-domain method. PubDate: 2018-04-23 DOI: 10.1007/s40314-018-0624-4
Authors:R. Naz; Azam Chaudhry Abstract: In this paper, we establish multiple closed-form solutions for all the variables in the Lucas–Uzawa model with externalities for the case with no parameter restrictions as well as for cases with specific parameter restrictions. These multiple solutions are derived with the help of the results derived in Naz et al. (Commun Nonlinear Sci Numer Simul 30(1):299–306, 2016) and Naz and Chaudhry (Math Modell Anal 22(4):464–483, 2017). This multiplicity of solutions is new to the economic growth literature on Lucas–Uzawa model with externalities. After finding solutions for the Lucas–Uzawa model with externalities, we use these solutions to derive the growth rates of all the variables in the system which enables us to fully describe the dynamics of the model. The multiple solutions can potentially explain why some countries economically overtake other countries even though they start from the same initial conditions. We have provided results of the numerical simulations procedure for \(\sigma =\beta \) . PubDate: 2018-04-19 DOI: 10.1007/s40314-018-0622-6
Authors:Razieh Dehghani; Narges Bidabadi; Mohammad Mehdi Hosseini Abstract: Using chain rule, we propose a modified secant equation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant equation we present a new BFGS method for solving unconstrained optimization problems. The proposed method makes use of both gradient and function values, and utilizes information from two most recent steps, while the usual secant relation uses only the latest step information. Under appropriate conditions, we show that the proposed method is globally convergent without convexity assumption on the objective function. Comparative numerical results show computational efficiency of the proposed method in the sense of the Dolan–Moré performance profiles. PubDate: 2018-04-19 DOI: 10.1007/s40314-018-0620-8
Authors:Yue Cao; Baoli Yin; Yang Liu; Hong Li Abstract: In this article, a second-order Crank–Nicolson weighted and shifted Grünwald integral (WSGI) time-discrete scheme combined with finite element method is studied for finding the numerical solution of the multi-dimensional time-fractional wave equation. The time-fractional wave equation with Caputo-fractional derivative is transformed into the time-fractional integral equation by integral technique, then the second-order Crank–Nicolson finite element scheme with a time second-order WSGI discrete approximation for fractional integral is formulated. The analysis of stability is made, then a priori error estimate is given by making use of the conversion technique between the WSGI formula and fractional integral. At the end of the article, some numerical examples covering two two-dimensional cases with rectangular element and triangular element and a three-dimensional case with tetrahedral element are shown to test and verify our theoretical results. PubDate: 2018-04-19 DOI: 10.1007/s40314-018-0626-2
Authors:B. Behzad; B. Ghazanfari; A. Abdi Abstract: In this paper, we study the construction and implementation of special Nordsieck second derivative general linear methods of order p and stage order \(q=p\) in which the number of input and output values is \(r=p\) rather than \(r=p+1\) . We will construct A- and L-stable methods of orders three and four in this form with Runge–Kutta stability properties. The efficiency of the constructed methods and reliability of the proposed error estimates are shown by implementing of the methods in a variable stepsize environment on some well-known stiff problems. PubDate: 2018-04-17 DOI: 10.1007/s40314-018-0619-1
Authors:G. N. Silva; P. S. M. Santos; S. S. Souza Abstract: In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341–347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295–313, 1986; Numer Math 51(5):545–557, 1987) and Robinson (Numer Math 19:341–347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results. PubDate: 2018-04-05 DOI: 10.1007/s40314-018-0617-3
Authors:Hanquan Wang; Zhenguo Liang; Ronghua Liu Abstract: We develop a splitting Chebyshev collocation (SCC) method for the time-dependent Schrödinger–Poisson (SP) system arising from theoretical analysis of quantum plasmas. By means of splitting technique in time, the time-dependant SP system is first reduced to uncoupled Schrödinger and Poisson equations at every time step. The space variables in Schrödinger and Poisson equations are next represented by high-order Chebyshev polynomials, and the resulting system are discretized by the spectral collocation method. Finally, matrix diagonalization technique is applied to solve the fully discretized system in one dimension, two dimensions and three dimensions, respectively. The newly proposed method not only achieves spectral accuracy in space but also reduces the computer-memory requirements and the computational time in comparison with conventional solver. Numerical results confirm the spectral accuracy and efficiency of this method, and indicate that the SCC method could be an efficient alternative method for simulating the dynamics of quantum plasmas. PubDate: 2018-03-31 DOI: 10.1007/s40314-018-0616-4
Authors:M. Chehlabi Abstract: In this paper, we study the continuity of solution functions to a class of fuzzy differential equations (FDEs) in the form \(y'(t)=\frac{\varphi (t)}{(t-\alpha )^{p}}\odot y(t)+\psi (t)\) , where the coefficient function \(\frac{\varphi (t)}{(t-\alpha )^{p}}\) is a discontinuous function at the point \(t=\alpha \) and \(\alpha \) is an inner point of the interval under study. At first, the continuity of solutions for the crisp case of the problem is investigated and those results are extended to the fuzzy case of the problem from the view point of strongly generalized differentiability (G-differentiability). Next, we obtain explicit formulas of solutions and the conditions of their existence for a special class of these problems. Finally, the results are illustrated by solving some examples. PubDate: 2018-03-31 DOI: 10.1007/s40314-018-0612-8
Authors:Tahir Mahmood; Muhammad Irfan Ali; Azmat Hussain Abstract: In the present paper, concept of roughness for fuzzy filters with thresholds \(\left( u_{1},u_{2}\right) \) in ordered semigroups is introduced. Then, this concept is extended to fuzzy bi-filters with thresholds and fuzzy quasi-filters with thresholds. Further approximations of fuzzy ideals with thresholds, fuzzy bi-ideals with thresholds, and fuzzy interior ideals with thresholds are studied. Moreover, this concept is applied to study approximations of fuzzy quasi-ideals with thresholds and semiprime fuzzy quasi-ideals with thresholds. PubDate: 2018-03-27 DOI: 10.1007/s40314-018-0615-5
Authors:Sulan Li Abstract: This article addresses the problem of robust stability and stabilization for linear fractional-order system with poly-topic and two-norm bounded uncertainties, and focuses particularly on the case of a fractional order α such that 1 < α < 2. First, the robust asymptotical stable condition is presented. Second, the design method of the state feedback controller for asymptotically stabilizing such uncertain fractional order systems is derived. In the proposed approach, linear matrix inequalities formalism is used to check and design. Lastly, two simulation examples are given to validate the proposed theoretical results. PubDate: 2018-03-26 DOI: 10.1007/s40314-018-0610-x
Authors:Nilson J. M. Moreira; Leonardo T. Duarte; Carlile Lavor; Cristiano Torezzan Abstract: A Euclidean distance matrix (EDM) is a table of distance-square between points on a k-dimensional Euclidean space, with applications in many fields (e.g., engineering, geodesy, economics, genetics, biochemistry, and psychology). A problem that often arises is the absence (or uncertainty) of some EDM elements. In many situations, only a subset of all pairwise distances is available and it is desired to have some procedure to estimate the missing distances. In this paper, we address the problem of missing data in EDM through low-rank matrix completion techniques. We exploit the fact that the rank of a EDM is at most \(k+2\) and does not depend on the number of points, which is, in general, much bigger then k. We use a singular value decomposition approach that considers the rank of the matrix to be completed and computes, in each iteration, a parameter that controls the convergence of the method. After performing a number of computational experiments, we could observe that our proposal was able to recover, with high precision, random EDMs with more than 1000 points and up to 98% of missing data in few minutes. In addition, our method required a smaller number of iterations when compared to other competitive state-of-art technique. PubDate: 2018-03-21 DOI: 10.1007/s40314-018-0613-7
Authors:Pathaithep Kumrod; Wutiphol Sintunavarat Abstract: In this work, we improve the Ri’s fixed point theorem in Ri (Indag Math 27:85–93, 2016) by creating the \(\varphi \) -fixed point version of such result in metric spaces. These results generalize and extend several well-known comparable results in the literature. Several applications and some examples of our theorems are also given. PubDate: 2018-03-20 DOI: 10.1007/s40314-018-0614-6
Authors:A. T. Assanova; Zh. M. Kadirbayeva Abstract: A linear two-point boundary value problem for a system of loaded differential equations with impulse effect is investigated. Values in the previous impulse points are taken into consideration in the conditions of impulse effect. The considered problem is reduced to an equivalent multi-point boundary value problem for the system of ordinary differential equations with parameters. A numerical implementation of parametrization method is offered using the Runge–Kutta method of 4th-order accuracy for solving the Cauchy problems for ordinary differential equations. The constructed numerical algorithms are illustrated by examples. PubDate: 2018-03-19 DOI: 10.1007/s40314-018-0611-9
Authors:Nehad Ali Shah; Thanaa Elnaqeeb; Shaowei Wang Abstract: In this paper, we analyze the effects of Dufour number and fractional-order derivative on unsteady natural convection flow of a viscous and incompressible fluid over an infinite vertical plate with constant heat and mass fluxes. The fractional constitutive model is obtained using fractional calculus approach. The Caputo fractional derivative operator is used in this problem. The dimensionless system of equations has been solved by employing Laplace transformation technique. Closed form solutions for concentration, temperature and velocity are presented in the form of Wright function and complementary error function. Effects of fractional and physical parameters on temperature and velocity profiles are illustrated graphically. PubDate: 2018-03-17 DOI: 10.1007/s40314-018-0606-6
Authors:Jose A. Martinez-Melchor; Victor M. Jimenez-Fernandez; Hector Vazquez-Leal; Uriel A. Filobello-Nino Abstract: This paper presents a methodology for optimizing pre-calculated collision-free paths of differential-drive wheeled robots. The main advantage of this methodology is that optimization is done by considering the kinematics and mechanical constraints of the mobile robot. In accordance to this proposal, the optimized path is achieved by applying recursively a local smoothing on an initial path which is originally modeled as a one-dimensional piecewise linear function. By this recursive smoothing, it can be ensured that the original piecewise linear function can be transformed into a smooth one that fulfill the constraints established by the kinematic equations of the wheeled mobile in terms of a minimum radius of curvature. As a result of this, a trajectory which guarantees lower power consumption and lower mechanical wear, is obtained. To show the better performance of the proposed approach, numerical simulation results are contrasted to those obtained from other reported methods with regards to path length, minimum radius of curvature, cross track error, continuity and resulting acceleration. PubDate: 2018-03-17 DOI: 10.1007/s40314-018-0602-x
Authors:Junli Zhang; Changjiang Bu Abstract: Nekrasov matrices and nonsingular H-matrices are closely related. In this paper, Nekrasov tensors and S-Nekrasov tensors are proved to be nonsingular \({\mathcal {H}}\) -tensors. And tensors are generalized Nekrasov tensors if and only if they are nonsingular \({\mathcal {H}}\) -tensors. Furthermore, an iterative criterion for identifying nonsingular \({\mathcal {H}}\) -tensors is provided. PubDate: 2018-03-17 DOI: 10.1007/s40314-018-0607-5
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