University of TabrizComputational Methods for Differential Equations2345-39825220170401Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials881025911ENFarshid MirzaeeFaculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran0000-0002-1429-2548Journal Article20170107In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations which can be solved by an appropriate numerical method such as Newton’s method. Also, we show that the proposed method is convergent. Some examples are provided to illustrate the applicability, efficiency and accuracy of the suggested scheme. Comparison of the proposed method with other previous methods shows that this method is very accurate.http://cmde.tabrizu.ac.ir/article_5911_e0ade60b77cb2f95092df545478f04e8.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825220170401A new approach on studying the stability of evolutionary game dynamics for financial systems1031166011ENNarges Talebi MotlaghControl Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, IranAmir Rikhtegar GhiasiControl Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, IranFarzad HashemzadehControl Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, IranSehraneh GhaemiControl Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, IranJournal Article20161031Financial market modeling and prediction is a difficult problem and drastic changes of the price causes nonlinear dynamic that makes the price prediction one of the most challenging tasks for economists. Since markets always have been interesting for traders, many traders with various beliefs are highly active in a market. The competition among two agents of traders, namely trend followers and rational agents, to gain the highest profit in market is formulated as a dynamic evolutionary game, where, the evolutionary equilibrium is considered to be the solution to this game. The evolutionarily stablity of the equilibrium points is investigated inspite of the prediction error of the expectation.http://cmde.tabrizu.ac.ir/article_6011_94343d3d340300caa3f9b4216d2424ef.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825220170401Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions1171406012ENParisa RahimkhaniDepartment of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, IranYadollah OrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, IranEsmail BabolianDepartment of Computer Science, Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, IranJournal Article20161110In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on which the fractional order integration of FLWs are easy to calculate. The approach is used this operational matrix with the collocation points to reduce the under study problem to system of algebraic equations. Convergence of the fractional-order Legendre wavelet basis is demonstrate. Illustrative examples are included to demonstrate the validity and applicability of the technique.http://cmde.tabrizu.ac.ir/article_6012_41565e9da3ef7f1d50237b20695692e6.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825220170401Solution of Troesch's problem through double exponential Sinc-Galerkin method1411576013ENMohammad NabatiDepartment of Basic Sciences, Abadan Faculty of Petroleum Engineering,
Petroleum University of Technology, Abadan, IranMahdi JalalvandDepartment of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20170104Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. Moreover, in order to illustrate the accuracy of presented method, the obtained results compared with numerical results in the open literature. The demonstrated results confirmed that proposed method was considerably efficient and accurate.http://cmde.tabrizu.ac.ir/article_6013_7f8f210d6d5b95f23cb319b0f61ae6b7.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825220170401Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations1581696077ENKamal ShahDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanSalman ZebDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanRahmat Ali KhanDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanJournal Article20170114This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞) is a continuous function. We use some classical results of fixed point theory to obtain sufficient conditions for the existence and multiplicity results of positive solutions to the problem under consideration. In order to show the applicability of our results, we provide some examples.http://cmde.tabrizu.ac.ir/article_6077_786926df406ec4f5042d803915a6e8dd.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825220170401A wavelet method for stochastic Volterra integral equations and its application to general stock model1701886086ENSaeed VahdatiDepartment of Mathematics,
Khansar Faculty of Mathematics and Computer Science, Khansar, IranJournal Article20160811In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation which can be solved by some numerical methods like Newton's or Broyden's methods. The capability of the simulation of Brownian motion with Schauder functions which are the integration of Haar functions enables us to find some reasonable approximate solutions. Two test examples and the application of the presented method for the general stock model are considered to demonstrate the efficiency, high accuracy and the simplicity of the presented method.http://cmde.tabrizu.ac.ir/article_6086_e150ecd516bdd8b7471d970f4fdb80a1.pdf