Journal of Mathematical Modeling
https://jmm.guilan.ac.ir/
Journal of Mathematical Modelingendaily1Fri, 20 May 2022 00:00:00 +0430Fri, 20 May 2022 00:00:00 +0430Numerical methods based on spline quasi-interpolation operators for integro-differential equations
https://jmm.guilan.ac.ir/article_5574.html
In this paper, we propose collocation and Kantorovich methods based on spline quasi-interpolants defined on a bounded interval &nbsp;to solve numerically a class of Fredholm integro-differential equations. We describe the computational aspects for calculating the approximate solutions and &nbsp;give theoretical results corresponding to the convergence order of each method in terms of the degree of the considered spline quasi-interpolant. Finally, we provide some numerical tests that confirm the theoretical results and prove the efficiency of the proposed methods.Solvability of the fuzzy integral equations due to road traffic flow
https://jmm.guilan.ac.ir/article_5580.html
In this research, we investigate the fuzzy integral equations related to traffic flow. Using the Banach fixed point theorem, we prove the existence and uniqueness of the solution for such equations. Using the Picard iterative method, we obtain the upper bound for an accurate and approximate solution. Finally, we obtain an error estimation between the exact solution and the solution of the iterative method. Example shows the applicabilityof our results.A mathematical model to simulate the drug release pattern from drug-eluting stents with biostable polymeric bulk and hydrophobic incorporated drug
https://jmm.guilan.ac.ir/article_5596.html
DES, or drug-eluting stents, have the advantage of reducing restenosis rates relative to bare-metal stents. Modeling and simulation can be used to improve device performance. In this study, a general mathematical model for releasing a hydrophobic drug from a drug-eluting stent, DES, with a biostable coating is modeled. Most mathematical models allow the drug in the polymer to be released freely. This is suitable when the initial concentration of the drug in the polymer is less than the solubility, in which case the dissolution of the drug can be considered instantaneously. On the other hand, matrix devices can be loaded above solubility to provide zero-order release. to this end, we have equipped a model with a function that determines how the dissolution processes change with the dispersed phase discharge. The general model is analyzed with some limitations, and it is reduced to a new model that is consistent with previous studies. We examine the effects of initial drug loading and dissolution rate constant in numerically solving one of the new models, which is novel in DESs.A posteriori error analysis for the Cahn-Hilliard equation
https://jmm.guilan.ac.ir/article_5726.html
The Cahn-Hilliard equation is discretized by a Galerkin finite element&nbsp; method based on continuous piecewise linear functions in space and discontinuous piecewise constant functions in time. A posteriori error&nbsp;estimates are proved by using the methodology of dual weighted residuals.A direct solver for solving systems of linear equations with banded ill-conditioned Toeplitz matrices
https://jmm.guilan.ac.ir/article_5729.html
In this paper, the banded Toeplitz matrices generated by $f(\theta)=(2(1-\cos(\theta-\tilde{\theta})))^d$ are studied. The function $f$ is a real non-negative function with a zero of order $2d$ at $\tilde{\theta}$ and the generated matrices are ill-conditioned Hermitian positive definite. We show that these banded Toeplitz matrices are similar to the banded real symmetric positive definite Toeplitz matrices that are generated by $f(\theta)=(2(1-\cos(\theta)))^d$. &nbsp;A fast direct solver is proposed to compute the inverse of these real matrices. Numerical experiments show that our proposed method is faster and more stable than the stable Levinson algorithm.Stable recovery of a space-dependent force function in a one-dimensional wave equation via Ritz collocation method
https://jmm.guilan.ac.ir/article_5731.html
In this paper, we consider the problem of approximating the displacement and the wave sink or source in a 1D wave equation from various measurements. First, the problem is recast as a certain hyperbolic equation. Then, we propose a Ritz approximation as the solution of the reformulated problem and apply the collocation method to convert the inverse problem to a system of linear equations. Since the problem is not well-posed, the numerical discretization of the problem may produce a system of equations that is not well-conditioned. Therefore, we apply the Tikhonov regularization method to obtain a stable solution. For the contaminated measurements, we take advantage of the mollification method in order to derive stable numerical derivatives. Several test examples are provided to show the effectiveness of the proposed technique for obtaining satisfactory results.Two efficient heuristic algorithms for the integrated production planning and warehouse layout problem
https://jmm.guilan.ac.ir/article_5732.html
In (Zhang et al. An integrated strategy for a production planning and warehouse layout problem: modeling and solution approaches, &nbsp;Omega 68 &nbsp;(2017) 85--94) &nbsp; &nbsp;the authors have proposed a mixed-integer linear programming model for the integrated production planning and warehouse layout problem. To solve the model, they proposed a Lagrangian relax-and-fix heuristic that takes significant amount of time to stop with gaps above 5$\%$ for large-scale instances. Here, we present two heuristic algorithms to solve the problem. In the first one, we use a greedy approach by allocating &nbsp;warehouse locations with less reservation &nbsp;costs, and also less &nbsp;transportation costs &nbsp;from the production area to locations and from locations to the output point &nbsp;to items with higher demands. Then a smaller model is solved. In the second heuristic, first we sort items in descending order according to the fraction of sum of the demands for that item in the time horizon plus the maximum demand for that item in the time horizon and &nbsp;sum of all its demands in the time horizon. Then we categorize the sorted items into groups of 3, 4, or 5, and solve a small-scale optimization problem for each group, hoping to improve the solution of the first heuristic. Our preliminary numerical results show &nbsp;the effectiveness of the proposed heuristics.Improving Canny edge detection algorithm using fractional-order derivatives
https://jmm.guilan.ac.ir/article_5755.html
One of the purposes of edge detection is to use methods that be able to process visual information according to human needs. Therefore, an edge detector is reliable when evaluated by measurement criteria before use in computer vision tools. These criteria compute the difference between the ground truth edge map (reference image) and the original image. In this study, we propose an improved Canny edge detection method based on the fractional-order operators to extract the ideal edge map. Then, by changing the hysteresis thresholds, the thin edges are obtained by filtering gradient calculations based on fractional-order masks. In addition, we employ common fractional-order derivative operators to extract the edge strength and enhance image edge contrast. The plotted curves of the edge detection criteria show that the obtained edge map of the proposed edge detection operator, which is considered to be the minimal rating of &nbsp;measurement, is visually and quantitatively closer to ground truth.Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation
https://jmm.guilan.ac.ir/article_5803.html
We develop a robust uniformly convergent numerical scheme for singularly perturbed time dependent Burgers-Huxley partial differential equation. We first discretize the time derivative of the equation using the Crank-Nicolson finite difference method. Then, the resulting semi-discretized nonlinear ordinary differential equations are linearized using the quasilinearization technique, and finally, design a fitted operator upwind finite difference method to resolve the layer behavior of the solution in the spatial direction. Our analysis has shown that the presented method is second order parameter uniform convergent in time and first order in space. Numerical experiments are conducted to validate the theoretical results.&nbsp;On the solution of parameterized Sylvester matrix equations
https://jmm.guilan.ac.ir/article_5808.html
In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and so the parameterized system of equations appears. This work considers the parameterized Sylvester matrix equations and tries to propose some methods containing a direct method and two iterative methods to obtain outer estimations of the solution set.WENO schemes with Z-type non-linear weighting procedure for fractional differential equations
https://jmm.guilan.ac.ir/article_5892.html
In this paper, a new fourth-order finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the fractional differential equations which may contain non-smooth solutions at a later time, even if the initial solution is smooth enough. A set of Z-type non-linear weights is constructed based on the $L_1$ norm, yielding improved WENO scheme with more accurate resolution. The Caputo fractional derivative of order $\alpha$ is split into a weakly singular integral and a classical second derivative. The classical Gauss-Jacobi quadrature is employed for solving the weakly singular integral. Also, a new WENO-type reconstruction methodology for approximating the second derivative is developed. Some benchmark examples are prepared to illustrate the efficiency, robustness, and good performance of this new finite difference WENO-Z scheme.Analysis of $GI/M/1/N$ and $GI/Geo/1/N$ queues with balking and vacation interruptions
https://jmm.guilan.ac.ir/article_5893.html
This paper addresses renewal input continuous &nbsp;and &nbsp;discrete time &nbsp;queues with balking and vacation interruptions. An arriving client may join the system or &nbsp;balk with some state-dependent probability. Whenever the server finds an empty system, he leaves for a working vacation. During working vacations, if there are clients to be served at a service completion instant, the server interrupts the &nbsp;working vacation and switches to regular service period. The embedded Markov chain technique has been adopted for evaluating pre-arrival epoch probabilities and &nbsp;supplementary variable approach is employed to evaluate arbitrary instant probabilities. Few performance characteristics and sojourn time distribution have also been demonstrated. Finally, &nbsp;numerical investigations have been figured out to depict the impact of the model variables on the performance indices.Improving Bitcoin price prediction power by time-scale decomposition and GMDH-type neural network: A comparison of different periods and features
https://jmm.guilan.ac.ir/article_5804.html
This paper aims to improve the predictability power of a machine learning method by proposing a two-stage prediction method. We use Group Modeling Data Handling (GMDH)-type neural network method to eliminate the user role in feature selection. To consider recent shocks in Bitcoin market, we consider three periods, before COVID-19, after COVID-19, and after Elon Musk's tweeter activity. Using time-scale analysis, we decomposed the data into different scales. We further investigate the forecasting accuracy across different frequencies. The findings show that in shorter period the first, second and third lag of daily prices and trade volume produce valuable information to predict Bitcoin price while the seven days lag can improve the prediction power over longer period. The results indicate a better performance of the wavelet base GMDH-neural network in comparison with the standard method. This reveals the importance of trade frequencies' impact on the forecasting power of models.Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons
https://jmm.guilan.ac.ir/article_5895.html
In this paper, a general class of fractional-order complex-valued bidirectional associative memory neural network with time delay is considered. This neural network model contains an arbitrary number of neurons, i.e. one neuron in the X-layer and other neurons in the Y-layer. Hopf bifurcation analysis of this system will be discussed. Here, the number of neurons, i.e., $n$ can be chosen arbitrarily. We study Hopf bifurcation by taking the time delay as the bifurcation parameter. The critical value of the time delay for the occurrence of Hopf bifurcation is determined. Moreover, we find two kinds of appropriate Lyapunov functions that under some sufficient conditions, global stability of the system is obtained. Finally, numerical examples are also presented.Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction
https://jmm.guilan.ac.ir/article_5899.html
This paper proposes a proximal difference-of-convex algorithm with extrapolation ($PDCA_e$) &nbsp;based on Dinkelbach's approach for the optimal correction of &nbsp;two types of piecewise linear systems, classical obstacle problems and equilibrium problems, and linear inequalities. Using &nbsp;Dinkelbach's theorem &nbsp;leads &nbsp;to getting &nbsp;the roots of two single-variable functions. Considering the non-convex and level-bounded properties of the obtained problems, we use a proximal difference-of-convex algorithm programming to solve them. The experimental results on several randomly generated test problems show that the $PDCA_e$-generalized Newton method &nbsp;outperforms other methods for both feasible and infeasible cases.Multi-agent single machine scheduling problem with transportation constraints
https://jmm.guilan.ac.ir/article_5244.html
A multi-agent single machine scheduling problem with transportation constraints is studied. We assume that there are several independent agents placed in different geographical locations, each of them has several orders and each order includes different types of products. We use a simple and effective model to obtain maximum profit of the products. To have desired on-time deliveries, the minimization of the transportation costs and total tardiness costs are considered as objective functions. The main idea of this research is to develop a simple and integrated scheduling and transportation model which can be applied in many factories, chain stores, and so on. In order to solve this problem, a mixed integer linear programming (MILP) model is presented. Moreover, since solving large instances of the proposed MILP model is very time-consuming, a heuristic algorithm is presented. Implementing of two approaches on a variety of datasets show that the heuristic algorithm can provide good-quality solutions in very short time.Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions
https://jmm.guilan.ac.ir/article_5295.html
In this paper, we use the rational radial basis function (RRBF) method for solving the one dimensional Sine-Gordon (SG) equation, especially the case with steep front or sharp gradient solutions. The time and spatial derivatives are approximated by the finite difference and RRBF method, respectively. Some numerical experiments are given in both perturbed and unperturbed cases, and are compared with some other numerical methods to confirm the good accuracy of the presented method. The conservation law of energy is also investigated.Bound-preserving interpolation using quadratic splines
https://jmm.guilan.ac.ir/article_5323.html
In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When&nbsp; &nbsp;function &nbsp;is known to be bounded, then it is &nbsp;natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods &nbsp; use quadratic splines as basis and involve solving a linear programming or a mixed integer linear &nbsp;programming problem which gives $C^1$ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability &nbsp;and&nbsp; applicability of &nbsp;the proposed techniques &nbsp;have been illustrated through examples.An improved upper bound for ultraspherical coefficients
https://jmm.guilan.ac.ir/article_5370.html
In this paper, new upper bounds for the ultraspherical coefficients of differentiable functions are presented. Using partial sums of ultraspherical polynomials, error approximations are presented to estimate differentiable functions. Also, an error estimate of the Gauss-Jacobi quadrature is obtained and we state an upper bound for Legendre coefficients which is sharper than upper bounds proposed so far. Numerical examples are given to assess the efficiency of the presented theoretical results.Optimal partition invariancy in multi-parametric linear optimization
https://jmm.guilan.ac.ir/article_5418.html
In a linear optimization problem, objective function, coefficients matrix, and the right-hand side might be perturbed with distinct parameters independently. For such a problem, we are interested in finding the region that contains the origin, and the optimal partition remains invariant. A computational methodology is presented here for detecting the boundary of this region. The cases where perturbation occurs only in the coefficients matrix and right-hand side vector or the objective function are specified as special cases. The findings are illustrated with some simple examples.A novel approach for modeling system reliability characteristics in an imprecise environment
https://jmm.guilan.ac.ir/article_5460.html
In this paper, we introduce and investigate a new definition for the density function of fuzzy random variables. Then, based on this definition, we give a new viewpoint on aging properties. To do this end, the concepts of the hazard rate function and mean residual function are investigated for the Exponential fuzzy random variable. Also, we obtain &nbsp;the aging properties of &nbsp;new Exponential fuzzy random variables based on existing methods. &nbsp;Finally, using a practical example, we illustrate the proposed approach and show that &nbsp;the performance of proposed &nbsp;approach is better than two other existing &nbsp;methods.An iterative variational model for blind image deconvolution
https://jmm.guilan.ac.ir/article_5461.html
Classical image deconvolution seeks an estimate of the true image when the blur kernel or the point spread function (PSF) of the blurring system is known a priori. However, blind image deconvolution addresses the much more complicated, but realistic problem where the PSF is unknown. Bayesian inference approach with appropriate priors on the image and the blur has been used successfully to solve this blind problem, in particular with a Gaussian prior and a joint maximum a posteriori (JMAP) estimation. However, this technique is unstable and suffers from significant ringing artifacts in various applications. To overcome these limitations, we propose a regularized version using $H^1$ regularization terms on both the sharp image and the blur kernel. We present also useful techniques for estimating the smoothing parameters.&nbsp; We were able to derive an efficient algorithm that produces high quality deblurred results compared to some well-known methods in the literature.A descent family of hybrid conjugate gradient methods with global convergence property for nonconvex functions
https://jmm.guilan.ac.ir/article_5482.html
In this paper, we present a new hybrid conjugate gradient method for unconstrained optimization that possesses sufficient descent property independent of any line search. In our method, a convex combination of the Hestenes-Stiefel (HS) and the Fletcher-Reeves (FR) methods, is used as the conjugate parameter and the hybridization parameter is determined by minimizing the distance between the hybrid conjugate gradient direction and direction of the three-term HS method proposed by M. Li (\emph{A family of three-term nonlinear conjugate gradient methods close to the memoryless BFGS method,} Optim. Lett. \textbf{12} (8) (2018) 1911--1927). Under some standard assumptions, the global convergence property on general functions is established. Numerical results on some test problems in the CUTEst library illustrate the efficiency and robustness of our proposed method in practice.&nbsp;A numerical method for solving stochastic linear quadratic problem with a finance application
https://jmm.guilan.ac.ir/article_5525.html
This paper is concerned with the stochastic linear quadratic regulator (LQR) optimal control problem in which dynamical systems have control-dependent diffusion coefficients. In fact, providing the solution to this problem leads to solving a matrix Riccati differential equation as well as a vector differential equation with boundary conditions. The present work mainly &nbsp;proposes not only a novel method but also an efficient fixed-point scheme based on the spline interpolation for the numerical solution to the stochastic LQR problem. Via implementing the proposed method to the corresponding differential equation of the stochastic LQR optimal control problem, not only is the numerical solution gained, but also a suboptimal control law is obtained. Furthermore, the method application is illustrated by means of an optimal control example with the financial market problems, including two investment options.Existence, uniqueness and stability results of an iterative survival model of red blood cells with a delayed nonlinear harvesting term
https://jmm.guilan.ac.ir/article_5541.html
In this article, a first-order iterative Lasota-Wazewska model with a&nbsp; nonlinear delayed harvesting term is discussed. Some sufficient conditions&nbsp; are derived for proving the existence, uniqueness and continuous dependence&nbsp; on parameters of positive periodic solutions with the help of&nbsp; Krasnoselskii's and Banach fixed point theorems along with the Green's&nbsp; functions method. Besides, at the end of this work, three examples are&nbsp; provided to show the accuracy of the conditions of our theoretical findings which are completely innovative and complementary to some earlier&nbsp; publications in the literature.Stochastic gradient-based hyperbolic orthogonal neural networks for nonlinear dynamic systems identification
https://jmm.guilan.ac.ir/article_5555.html
Orthogonal neural networks (ONNs) are some &nbsp;powerful types of the neural networks in the modeling of non-linearity. They are constructed by the usage &nbsp;of orthogonal functions sets. Piecewise continuous orthogonal functions (PCOFs) are some important classes of orthogonal functions. In this work, based on a set of hyperbolic PCOFs, we propose the hyperbolic ONNs &nbsp;to identify the nonlinear dynamic systems. We train the proposed neural models with the stochastic gradient descent learning algorithm. Then, we prove the stability of this algorithm. Simulation results show the efficiencies of proposed model.Numerical solution of space-time variable fractional order advection-dispersion equation using radial basis functions
https://jmm.guilan.ac.ir/article_5561.html
This paper aims to advance the radial basis function method for solving space-time variable-order fractional partial differential equations. The fractional derivatives for time and space are considered in the Coimbra and the Riemann-Liouville sense, respectively. First, the time-variable fractional derivative is discretized through a finite difference approach. Then, the space-variable fractional derivative is approximated by radial basis functions. Also, we advance the Rippa algorithm to obtain a good value for the shape parameter of the radial basis functions. Results obtained from numerical experiments have been compared to the analytical solutions, which indicate high accuracy and efficiency for the proposed scheme.