فهرست مطالب

Mathematical Modeling - Volume:9 Issue: 2, Spring 2021
  • Volume:9 Issue: 2, Spring 2021
  • تاریخ انتشار: 1400/01/31
  • تعداد عناوین: 12
|
  • Nayyer Mehanfar, Alireza Ghaffari Hadigheh * Pages 145-172
    In this study, we consider a family of uni-parametric linear optimization problems that the objective function, the right, and the left hand side of constraints are linearly perturbed with an identical parameter. We are interested in studying the effect of this variation on a given optimal solution and the behavior of the optimal value function on its domain.  This problem has several applications, such as in linear time dynamical systems.  A  prototype example is provided in dynamical systems as a justification for the practicality of the study results. Based on the concept of induced optimal partition, we identify the intervals for the parameter value where optimal induced partitions are invariant.  We show that the optimal value function is piecewise fractional continuous in the interior of its domain, while it is not necessarily to be continuous at the endpoints. Some concrete examples depict the results of the analysis.
    Keywords: Uni-parameter linear optimization, Induced optimal partition invariancy analysis, change point, Moore-Penrose inverse, Realization theory
  • Gus Argyros, Michael Argyros, Ioannis Argyros, Santhosh George * Pages 173-183
    There is a plethora of third and fourth convergence order algorithms  for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or  uniqueness of the solution results if given at all are also based on the existence of high order derivatives. But these problems limit the applicability  of the algorithms. That is why we address all these problems under  conditions only on the first derivative that appear in these algorithms. Our analysis includes computable error estimations as well as uniqueness results based on $omega-$ continuity conditions on the Fr'echet derivative of the operator involved.
    Keywords: $omega-$ continuity, ball of convergence, Algorithm
  • Zahra Dehghan, Jalil Rashidinia * Pages 185-199
    Two different methods based on radial basis functions (RBFs) for one-dimensional Kawahara equation are presented. In the first one, we use  MQ-RBF with predictor-corrector scheme.  Then the statistical tool LOOCV is implemented  for selecting good value of shape parameter. In the second one a different scheme is constructed for time and  then the RBF-QR method is implemented.  In the both of two approaches, the Not-a-Knot method is used to improve the accuracy at the boundaries. The purpose of this paper is to devot suitable strategies to obtain more accurate and efficient solutions specially for arising fifth order time-dependent nonlinear equations comparing with the results from the relevant papers.
    Keywords: Kawahara equation, multiquadric Radial basis functions, theta-weighted scheme, RBF-QR, LOOCV strategy
  • Majid Erfanian *, Hamed Zeidabadi Pages 201-213
    We successively apply the rational Haar wavelet  to solve the nonlinear Volterra integro-differential equations and nonlinear Fredholm integro-differential equations. Using the Banach fixed point theorem for these equations, we prove the convergence. In this method, no numerical integration is used. Numerical results are presented to show the effectiveness of this method.
    Keywords: Fixed point Banach theorem, nonlinear, Volterra, Fredholm, integro-differential, Haar wavelet, Convergence
  • Seyed Amin Badri *, Allahyar Daghbandan, Zahra Aghabeiginiyay Fatalaki, Mohammad Mirzazadeh Pages 215-227
    Given the reduction of non-renewable energy resources and increase of energy costs during  recent years, developing an efficient scheduling model considering energy consumption is necessary in manufacturing systems. This paper is dedicated to flow shop scheduling problem under Time-Of-Use electricity tariffs. In this regard, a bi-objective mixed-integer programming model is formulated for the problem. Two objectives, namely, the minimization of the total electricity cost and the sum of earliness and tardiness of jobs, are considered simultaneously. The bi-objective model is converted into an equivalent single objective linear programming model using fuzzy multi-objective programming approach. The CPLEX solver in GAMS software is used to solve the proposed model for an instance. The numerical example shows that the proposed model is reasonable and applicable.
    Keywords: mixed-integer programming, bi-objective model, electricity price, earliness, tardiness
  • Alexander Balandin * Pages 229-238
    This paper studies  a problem of inverse scattering  on the basis of maximum entropy principle. The advantage of the method implies  maximization of the entropy functional, what is the main condition and the scattering data and any a priory information are considered as constraints. This rephrasing of the problem leads to significant simplifications, since the entropy functional is known to be concave. Other peculiar properties of the method include his stability to various kinds of artifacts and adaptability to various schemes of measurement.
    Keywords: inverse problems, maximum entropy, cone ray transform, computerized tomography
  • Zohreh Ramezani, Faezeh Toutounian * Pages 239-256
    The CMRH (Changing Minimal Residual method based on the Hessenberg process) is an iterative method for solving nonsymmetric linear systems. The method generates a Krylov subspace in which   an approximate solution is determined.  The CMRH method is generally used with restarting to reduce the storage. Restarting often slows down the convergence.  In this paper we present  augmentation and deflation techniques for  accelerating  the convergence of the restarted CMRH method.  Augmentation adds a subspace to the Krylov subspace, while deflation removes certain parts from the operator.  Numerical experiments show that the new algorithms can be  more efficient compared with CMRH method.
    Keywords: Krylov subspace methods, augmentation, deflation, CMRH method, GMRES method, harmonic Ritz values
  • Kapula Rajendra Prasad, Mahammad Khuddush *, Mahanty Rashmita Pages 257-275
    In this paper, we establish the existence of denumerably many positive solutions for singular iterative system of fractional order boundary value problem involving Riemann--Liouville integral boundary conditions with increasing homeomorphism and positive homomorphism operator by using H"{o}lder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space.
    Keywords: Denumerable, positive solutions, fractional derivative, homeomorphism, homomorphism, Fixed point theorem
  • Maryam Alipour, Samaneh Soradi-Zeid * Pages 277-291
    This paper is devoted to solve a set of non-linear optimal control problems which are touched with time-delay  Fredholm integro-differential equations. The serious objective of this work  is to contribute  an appropriate   direct scheme for solving these problems. The technique used  in this paper  is based upon the Dickson polynomials and collocation points. Getting through the solutions, the states and controls variables can be approximated with  Dickson polynomials. Therefore, the  optimal control problem with  time-delay   integro-differential equation   transforms  into a system of algebraic equations that by solving it, we can obtain the unknown coefficients of the main problem. The residual  error estimation of this technique is also investigated. Accuracy amount of the absolute errors have been studied for the performance of this method by solving several non-trivial examples.
    Keywords: Optimal control problems, Dickson polynomials, Time-delay equation, Fredholm integrao-differential equation, collocation points
  • Maryam Shams Solary * Pages 293-302
    We investigate the eigenvalue distribution of banded Hankel matrices with non-zero skew diagonals. This work uses push-forward of an arcsine density, block structures and generating functions. Our analysis is done by a combination of Chebyshev polynomials, Laplacian determinant expansion and mathematical induction.
    Keywords: Hankel, eigenvalue, Distribution, generating function
  • Zahra Noeiaghdam, Morteza Rahmani *, Tofigh Allahviranloo Pages 303-322
    The aim of this study is the introduction of the numerical methods for solving the fuzzy $q$-differential equations that many real life problems can be modelized in the form of these equations. $q$-Taylor's expansion method is among important and famous methods for solving these problems. In this paper, applications of the fuzzy $q$-Taylor's expansion, the fuzzy local $q$-Taylor's expansion and the fuzzy $q$-Euler's method, based on the generalized Hukuhara $q$-differentiability are illustrated which are two numerical methods for finding approximate solution of the fuzzy initial value $q$-problems (for short FIVq-Ps).
    Keywords: Generalized Hukuhara $q$-derivative, fuzzy $q$-Taylor's theorem, fuzzy local $q$-Taylor's expansion, fuzzy $q$-Euler's method
  • Arezo Ameri, Fatemeh Panjeh Ali Beik * Pages 323-330
    The minimum residual HSS (MRHSS) method is proposed in [BIT Numerical Mathematics, 59 (2019) 299--319] and its convergence analysis is proved under a certain condition. More recently in [Appl. Math. Lett. 94 (2019) 210--216], an alternative version of MRHSS is presented which converges unconditionally. In general, as the second approach works with a weighted inner product, it consumes more CPU time than MRHSS to converge. In the current work, we revisit the convergence analysis of the MRHSS method using a different strategy and state the convergence result for general two-step iterative schemes. It turns out that a special choice of parameters in the MRHSS results in an unconditionally convergent method without using a weighted inner product. Numerical experiments confirm the validity of established results.
    Keywords: Minimum residual technique, Hermitian, skew-Hermitian splitting, two-step iterative method, Convergence