University of TabrizComputational Methods for Differential Equations2345-39829220210401A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth3273461035310.22034/cmde.2020.31455.1472ENMinaBagherpoorfardDepartment of applied mathematics, Ferdowsi university of Mashhad, Mashhad. Iran.Ali RezaSoheiliDepartment of applied mathematics, Ferdowsi university of Mashhad, Mashhad, Iran.Journal Article20190110Using adaptive mesh methods is one of the strategies to improve numerical solutions in time dependent partial differential equations. The moving mesh method is an adaptive mesh method, which, firstly does not need an increase in the number of mesh points, secondly reduces the concentration of points in the steady areas of the solutions that do not need a high degree of accuracy, and finally places the points in the areas, where a high degree of accuracy is needed. In this paper, we improved the numerical solutions for a three-phase model of avascular tumor growth by using the moving mesh method. The physical formulation of this model uses reaction-diffusion dynamics with the mass conservation law and appears in the format of the nonlinear system of partial differential equations based on the continuous density of three proliferating, quiescent, and necrotic cell categorizations. Our numerical results show more accurate numerical solutions, as compared to the corresponding fixed mesh method. Moreover, this method leads to the higher order of numerical convergence.https://cmde.tabrizu.ac.ir/article_10353_c30e275526321601a1a6fc5896291675.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints3473571035210.22034/cmde.2020.30733.1459ENHadisMokhtavayiDepartment of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran.AghilehHeidariDepartment of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran.NaderKanziDepartment of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran.Journal Article20181205We consider a nonsmooth optimization problem with a feasible set defined by vanishing constraints. First, we introduce a constraint qualification for the problem, named NNAMCQ. Then, NNAMCQ is applied to obtain a necessary M-stationary condition. Finally, we present a sufficient condition for M-stationarity, under generalized convexity assumption. Our results are formulated in terms of Mordukhovich subdifferential.https://cmde.tabrizu.ac.ir/article_10352_0b6a2959c2b43ba7461b1c2201c089da.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system3583741032210.22034/cmde.2019.30396.1450ENElyasShivanianDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.AhmadJafarabadiDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.Journal Article20181115In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction-diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The effect of parameters and conditions are studied by considering the well known Brusselator model. Two test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme.https://cmde.tabrizu.ac.ir/article_10322_fb26a63e2c917e8049427f3c3ecd2a63.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback3753921032510.22034/cmde.2020.33660.1544ENSakineh BigomMirassadiFaculty of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Iran.HojjatAhsani TehraniFaculty of Mathematical Sciences, Shahrood University of Technology,
Shahrood, Iran.nullJournal Article20190523In this paper, we present a nonlinear parametric method to stabilize descriptor fractional discrete time linear system practically. Parametric methods with the free parameters can be adjusted to obtain better performance responses like minimum norm in state feedback. The aim is assigning desirable eigenvalues to obtain satisfactory responses by forward state feedback and forward and propositional state feedback in new systems with large matrices. However, finding the solution to nonlinear parametric equations makes some errors. In partial eigenvalue assignment, just a part of the open-loop spectrum of the standard linear systems is reassigned, while leaving the rest of the spectrum invariant. The size of matrices, state, and input vectors are decreased and the stability is kept. At the end, summary and conclusions are proposed and the convergence of state vectors in the descriptor fractional discrete-time system to zero is also shown by figures in a numerical example. Our method is also compared with another method with one of orthogonality relations in our article and example.https://cmde.tabrizu.ac.ir/article_10325_664a2b3731a01c3a36e6f95c75d95b79.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Solving some stochastic differential equation using Dirichlet distributions3933981032410.22034/cmde.2019.32914.1533ENHawreHadadDepartment of Statistics, Sciences and Research branch, Islamic Azad University, Tehran, Iran.HazhirHomeiDepartment of Statistic
University of Tabriz
P.O.Box 51666-16471
Tabriz, Iran.Mohammad HassanBehzadiDepartment of Statistics, Sciences and Research branch, Islamic Azad University, Tehran, Iran.RahmanFarnooshSchool of Mathematics ,Iran University of Science and
Technology, Tehran, Iran.Journal Article20190428Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients have Dirichlet distributions. A method is provided for calculating the distribution of these combinations which has been studied before. Our main result is the same as but from a different point of view.https://cmde.tabrizu.ac.ir/article_10324_cc28d04aa0f66ed68800b2c95ebd51c7.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Hyperbolic Ricci-Bourguignon flow3994091032710.22034/cmde.2020.34205.1566ENShahroudAzamiDepartment of pure Mathematics, Faculty of Sciences
Imam Khomeini International University,
Qazvin, Iran.Journal Article20190623In this paper, we consider the hyperbolic Ricci-Bourguignon flow on a compact manifold M and show that this flow has a unique solution on short-time with imposing on initial conditions. After then, we find evolution equations for Riemannian curvature tensor, Ricci curvature tensor and scalar curvature of M under this flow. In the final section, we give some examples of this flow on some compact manifolds.https://cmde.tabrizu.ac.ir/article_10327_4eed60752e4234f9632a77115adc98e9.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems4104261035110.22034/cmde.2020.29291.1412ENMaryamDehghanDepartment of Mathematics, Faculty of Sciences,
Persian Gulf University, Bushehr 75169, Iran.SaeedKarimi JafarbiglooDepartment of Mathematics, Faculty of Sciences,
Persian Gulf University, Bushehr 75169, Iran.Journal Article20180911In this paper, we concern ourselves with the study of a class of stationary states for reaction-diffusion systems with densities having disjoint supports. Major contribution of this work is computing the numerical solution of problem as the rate of interaction between two different species tend to infinity. The main difficulty is the nonlinearity nature of problem. To do so, an efficient iterative method is proposed by hybrid of the radial basis function (RBF) collocation and finite difference (FD) methods to approximate the solution. Numerical results with good accuracies are achieved where the shape parameter is carefully selected. Finally, some numerical examples are given to illustrate the good performance of the method.https://cmde.tabrizu.ac.ir/article_10351_eb1d75eb88216a96cbd77deb15a0c1f1.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Global dynamics and numerical bifurcation of a bioeconomic system4274451033210.22034/cmde.2020.29491.1421ENZeynabLajmiriSama technical and vocational training college,
Islamic Azad Univercity Izeh Branch, Izeh, Iran.ImanOrakSama technical and vocational training college,
Islamic Azad Univercity Izeh Branch, Izeh, Iran.RezaFereidooniReserch and development manager of oxin steel company of khozestan, Iran.Journal Article20180923A predator-prey model was extended to include nonlinear harvesting of the predator guided by its population, such that harvesting is only implemented if the predator population exceeds an economic threshold. Theoretical results showed that the harvesting system undergoes multiple bifurcations, including fold, supercritical Hopf, Bogdanov-Takens and cusp bifurcations. We determine stability and dynamical behaviors of the equilibrium of this system. Numerical simulation results are given to support our theoretical results.https://cmde.tabrizu.ac.ir/article_10332_935c51f0a6ec1c419007b446bea20387.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components4464661033010.22034/cmde.2020.34992.1598ENVahidTaherpourDepartment of Mathematics, Khorram Abad Branch, Islamic Azad University, Khorram Abad, IranMojtabaNazariDepartment of Mathematics, Khorram Abad Branch, Islamic Azad University,
Khorram Abad, Iran0000-0002-0166-8147AliNematiYoung Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran0000-0002-1263-345XJournal Article20190806In this paper, a numerical method is developed and analyzed for solving a class of fractional optimal control problems (FOCPs) with vector state and control functions using polynomial approximation. The fractional derivative is considered in the Caputo sense. To implement the proposed numerical procedure, the Ritz spectral method with Bernoulli polynomials basis is applied. By applying the Bernoulli polynomials and using the numerical estimation of the unknown functions, the FOCP is reduced to solve a system of algebraic equations. By rigorous proofs, the convergence of the numerical method is derived for the given FOCP. Moreover, a new fractional operational matrix compatible with the proposed spectral method is formed to ease the complexity in the numerical computations. At last, several test problems are provided to show the applicability and effectiveness of the proposed scheme numerically.https://cmde.tabrizu.ac.ir/article_10330_cab7ffd5a82352b18833673d5b555aaa.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Analytical solution for descriptor system in partial differential equations4674791268610.22034/cmde.2021.42195.1824ENSvetlana PetrovnaZubovaDepartment of mathematical Analysis, Faculty of Mathematics,\\Voronezh State University, Voronezh, Russia.Abdulftah HosniMohamadDepartment of mathematical Analysis, Faculty of Mathematics,\\Voronezh State University, Voronezh, Russia.0000-0003-1087-0512Journal Article20201009We consider a first-order partial differential equation with constant irreversible coefficients in a Banach space in the regular case. The equation is split into equations in subspaces, in which non-degenerate subsystems are obtained. We obtain an analytical solution of each system with Showalter-type conditions. Finally, an example is given to illustrate the theoretical<br /> results.https://cmde.tabrizu.ac.ir/article_12686_425b7d32c369dafd54ba4f58a734c16b.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Solving a class of fractional optimal control problems via a new efficient and accurate method4804921032910.22034/cmde.2020.35875.1620ENSamanehSoradi-ZeidFaculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, IranJournal Article20191015The present paper aims to get through a class of fractional optimal control problems (FOCPs). Furthermore, the fractional derivative portrayed in the Caputo sense through the dynamics of the system as fractional differential equation (FDE). Getting through the solution, firstly the FOCP is transformed into a functional optimization problem. Then, by using known formulas for computing fractional derivatives of Legendre wavelets (LWs), this problem has been reduce to an equivalent system of algebraic equations. In the next step, we can simply solved this algebraic system. In the end, some examples are given to bring about the validity and applicability of this technique and the convergence accuracy.https://cmde.tabrizu.ac.ir/article_10329_520124cea04625086027797c8505b9d3.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401On the numerical treatment and analysis of Hammerstein integral equation4935101033110.22034/cmde.2019.29825.1435ENMaryamDerakhshanepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili,
56199-11367, Ardabil, Iran.MohammadZarebniaepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili,
56199-11367, Ardabil, Iran.Journal Article20181015In this paper, we study the quadratic rules for the numerical solution of Hammerstein integral equation based on spline quasi-interpolant. Also the convergence analysis of the methods are given. The theoretical behavior is tested on examples and it is shown that the numerical results confirm theoretical part.https://cmde.tabrizu.ac.ir/article_10331_816a1327f4cbe60319bde09568c7ce14.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Solving brachistochrone problem via scaling functions of Daubechies wavelets5115221033310.22034/cmde.2020.34778.1588ENAzadKasnazaniDepartment of Applied Mathematics,
University of Kurdistan, Sanandaj, Iran.AmjadAliPanahDepartment of Applied Mathematics,
University of Kurdistan, Sanandaj, Iran.Journal Article20190722In this paper, we proposed an effective method based on the scaling function of Daubechies wavelets for the solution of the brachistochrone problem. An analytic technique for solving the integral of Daubechies scaling functions on dyadic intervals is investigated and these integrals are used to reduce the brachistochrone problem into algebraic equations. The error estimate for the brachistochrone problem is proposed and the numerical results are given to verify the effectiveness of our method.https://cmde.tabrizu.ac.ir/article_10333_25aa5d83406bfd2b13f545e6bfc2efd3.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options5235521033510.22034/cmde.2020.36000.1623ENMaryamRezaei MirarkolaeiFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.0000-0001-9626-5801AhmadrezaYazdanianFaculty of Finance Sciences
Kharazmi University, Tehran, Iran.Seyed MahdiMahmoudiFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, IranAliAshrafiFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, IranJournal Article20191008The Black-Scholes equation is one of the most important mathematical models in option pricing theory, but this model is far from market realities and cannot show memory effect in the financial market. This paper investigates an American option based on a time-fractional Black-Scholes equation under the constant elasticity of variance (CEV) model, which parameters of interest rate and dividend yield supposed as deterministic functions of time, and the price change of the underlying asset follows a fractal transmission system. This model does not have a closed-form solution; hence, we numerically price the American option by using a compact difference scheme. Also, we compare the time-fractional Black-Scholes equation under the CEV model with its generalized Black-Scholes model as α = 1 and β = 0. Moreover, we demonstrate that the introduced difference scheme is unconditionally stable and convergent using Fourier analysis. The numerical examples illustrate the efficiency and accuracy of the introduced difference scheme.https://cmde.tabrizu.ac.ir/article_10335_264b729cd71d9f412f817b6d5634349e.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401A Laguerre approach for solving of the systems of linear differential equations and residual improvement5535761075410.22034/cmde.2020.34871.1591ENSuayipYuzbasiDepartment of Mathematics, Faculty of Science,
Akdeniz University, TR 07058 Antalya, Turkey.0000-0002-5838-7063GamzeYildirimDepartment of Mathematics, Faculty of Science,
Akdeniz University, TR 07058 Antalya, Turkey.Journal Article20190726In this study, a collocation method based on Laguerre polynomials is presented to numerically solve systems of linear differential equations with variable coefficients of high order. The method contains the following steps. Firstly, we write the Laguerre polynomials, their derivatives, and the solutions in matrix form. Secondly, the system of linear differential equations is reduced to a system of linear algebraic equations by means of matrix relations and collocation points. Then, the conditions in the problem are also written in the form of matrix of Laguerre polynomials. Hence, by using the obtained algebraic system and the matrix form of the conditions, a new system of linear algebraic equations is obtained. By solving the system of the obtained new algebraic equation, the coefficients of the approximate solution of the problem are determined. For the problem, the residual error estimation technique is offered and approximate solutions are improved. Finally, the presented method and error estimation technique are demonstrated with the help of numerical examples. The results of the proposed method are compared with the results of other methodshttps://cmde.tabrizu.ac.ir/article_10754_4483e85df27b4d22c0556be887767d7a.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Analysis of time delay model for drug therapy on HIV dynamics5775881075610.22034/cmde.2020.34812.1589ENVinothSivakumarDepartment of Mathematics,
Sri Ramakrishna Mission Vidyalaya
College of Arts and Science,India.DumitruBaleanuCankaya University, Turkey.
Institute of Space Sciences, Romania.JayakumarThippanDepartment of Mathematics,
Sri Ramakrishna Mission Vidyalaya
College of Arts and Science,India.Prasantha BharathiDhandapaniDepartment of Mathematics,
Sri Ramakrishna Mission Vidyalaya
College of Arts and Science ,India.0000-0002-3152-1592Journal Article20190723We present and investigate the delayed model of HIV infection for drug therapy. The stability of the equilibrium states, disease free and infected equilibrium states are derived and the existence of Hopf bifurcation analysis is studied. We show that the system is asymptotically stable and the stability is lost in a range due to length of the delay, then Hopf bifurcation occurs when τ exceeds the critical value. At last numerical simulations are provided to verify the theoretical results.https://cmde.tabrizu.ac.ir/article_10756_e2ec139da13432d8a198743857fbd386.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities5896031060710.22034/cmde.2020.32848.1526ENNguyen ThanhChungDepartment of Mathematics, Quang Binh University,
312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Viet Nam.Journal Article20190414In this paper, we study the existence of a nontrival weak solution for a class of Kirchhoff type problems with singular potentials and critical exponents. The proofs are essentially based on an appropriated truncated argument, Caffarelli-Kohn-Nirenberg inequalities, combined with a variant of the concentration compactness principle. We also get a priori estimates of the obtained solutionhttps://cmde.tabrizu.ac.ir/article_10607_7e754b671a24766e874bbd6414d28cb7.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Stability in distribution of neutral stochastic functional differential equations with infinite delay6046221064310.22034/cmde.2020.32804.1525ENHusseinAskerDepartment of Mathematics,
Faculty of Computer Science and Mathematics,
Kufa University, Al-Najaf, Iraq.Journal Article20190411In this paper, we investigate stability in distribution of neutral stochastic functional differential equations with infinite delay (NSFDEwID) at the state space Cr. We drive a sufficient strong monotone condition for the existence and uniqueness of the global solutions of NSFDEwID in the state space Cr. We also address the stability of the solution map xt and illustrate the theory with an examplehttps://cmde.tabrizu.ac.ir/article_10643_7c762f6191c3073e1dcf6c81c074beab.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay6236361075310.22034/cmde.2020.35546.1608ENErhanPişkinDicle University, Department of Mathematics, Diyarbakir, Turkey.HazalYuksekkayaDicle University, Department of Mathematics, Diyarbakir, Turkey.Journal Article20190909In this work, we consider a logarithmic nonlinear viscoelastic wave equation with a delay term in a bounded domain. We obtain the local existence of the solution by using the Faedo-Galerkin approximation. Then, under suitable conditions, we prove the blow up of solutions in finite time.https://cmde.tabrizu.ac.ir/article_10753_17541edaeca34daeb0b2eafaedcf445e.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39829220210401Bounds of Riemann-Liouville fractional integral operators6376481075210.22034/cmde.2020.32653.1516ENGhulamFaridDepartment of Mathematics,
COMSATS University Islamabad,
Attock Campus, Attock, Pakistan.Journal Article20190325Fractional integral operators play an important role in generalizations and extensions of various subjects of sciences and engineering. This research is the study of bounds of Riemann-Liouville fractional integrals via (h − m)-convex functions. The author succeeded to find upper bounds of the sum of left and right fractional integrals for (h − m)-convex function as well as for functions which are deducible from aforementioned function (as comprise in Remark 1.2). By using (h − m) convexity of |f ′ | a modulus inequality is established for bounds of Riemann-Liouville fractional integrals. Moreover, a Hadamard type inequality is obtained by imposing an additional condition. Several special cases of the results of this research are identified. https://cmde.tabrizu.ac.ir/article_10752_c4ec191093d776940f3007fc1d6f70fe.pdf