University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials
88
102
EN
Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
f.mirzaee@malayeru.ac.ir
In 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.
Fredholm-Volterra integral equation,Bell polynomials,Collocation method,Operational matrix,Error analysis
http://cmde.tabrizu.ac.ir/article_5911.html
http://cmde.tabrizu.ac.ir/article_5911_e0ade60b77cb2f95092df545478f04e8.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
A new approach on studying the stability of evolutionary game dynamics for financial systems
103
116
EN
Narges
Talebi Motlagh
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
n.talebi@tabrizu.ac.ir
Amir
Rikhtegar Ghiasi
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
agiasi@tabrizu.ac.ir
Farzad
Hashemzadeh
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
hashemzadeh@tabrizu.ac.ir
Sehraneh
Ghaemi
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
ghaemi@tabrizu.ac.ir
Financial 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.
Heterogeneous Agent Model,Adaptive Belief System,Evolutionary Game Theory,Rational Agent,Evolutionary Stable Strategies
http://cmde.tabrizu.ac.ir/article_6011.html
http://cmde.tabrizu.ac.ir/article_6011_94343d3d340300caa3f9b4216d2424ef.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions
117
140
EN
Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
p.rahimkhani@alzahra.ac.ir
Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
ordokhani2000@yahoo.com
Esmail
Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
babolian@khu.ac.ir
In 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.
Fractional-order Legendre wavelets,Fractional differential equations,Collocation method,Caputo derivative,Operational matrix
http://cmde.tabrizu.ac.ir/article_6012.html
http://cmde.tabrizu.ac.ir/article_6012_41565e9da3ef7f1d50237b20695692e6.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
Solution of Troesch's problem through double exponential Sinc-Galerkin method
141
157
EN
Mohammad
Nabati
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering,
Petroleum University of Technology, Abadan, Iran
nabati@put.ac.ir
Mahdi
Jalalvand
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
m.jalalvand@scu.ac.ir
Sinc-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.
Sinc Function,Galerkin method,Double exponential transformation,Nonlinear Troesch's problem,BVP
http://cmde.tabrizu.ac.ir/article_6013.html
http://cmde.tabrizu.ac.ir/article_6013_7f8f210d6d5b95f23cb319b0f61ae6b7.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
158
169
EN
Kamal
Shah
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
kamalshah408@gmail.com
Salman
Zeb
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
salmanzeb@gmail.com
Rahmat Ali
Khan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
rahmat_alipk@yahoo.com
This 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.
Fractional differential equations,Boundary value problems,Positive solutions,Green’s function,fixed point theorem
http://cmde.tabrizu.ac.ir/article_6077.html
http://cmde.tabrizu.ac.ir/article_6077_786926df406ec4f5042d803915a6e8dd.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
2
2017
04
01
A wavelet method for stochastic Volterra integral equations and its application to general stock model
170
188
EN
Saeed
Vahdati
Department of Mathematics,
Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
sdvahdati@gmail.com
In 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.
Wavelets,Brownian Motion,Stochastic integral equation,Stochastic differential equation,Ito integral
http://cmde.tabrizu.ac.ir/article_6086.html
http://cmde.tabrizu.ac.ir/article_6086_e150ecd516bdd8b7471d970f4fdb80a1.pdf