2017
5
2
2
0
Numerical solution of nonlinear FredholmVolterra integral equations via Bell polynomials
2
2
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 FredholmVolterra 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.
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88
102


Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 6571995863, Malayer, Iran.
Faculty of Mathematical Sciences and Statistics,
I. R. Iran
f.mirzaee@malayeru.ac.ir
FredholmVolterra integral equation
Bell polynomials
Collocation method
Operational matrix
Error analysis
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A new approach on studying the stability of evolutionary game dynamics for financial systems
2
2
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.
1

103
116


Narges
TalebiMotlagh
University of Tabriz
University of Tabriz
I. R. Iran
n.talebi@tabrizu.ac.ir


Amir
Ghiasi
University of Tabriz
University of Tabriz
I. R. Iran
agiasi@tabrizu.ac.ir


Farzad
Hashemzadeh
University of Tabriz
University of Tabriz
I. R. Iran
hashemzadeh@tabrizu.ac.ir


Sehraneh
Ghaemi
University of Tabriz
University of Tabriz
I. R. Iran
ghaemi@tabrizu.ac.ir
Heterogeneous Agent Model
Adaptive Belief System
Evolutionary Game Theory
Rational Agent
Evolutionary Stable Strategies
Fractionalorder Legendre wavelets and their applications for solving fractionalorder differential equations with initial/boundary conditions
2
2
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 fractionalorder Legendre wavelets and operational matrix of fractionalorder integration. First the fractionalorder 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 fractionalorder Legendre wavelet basis is demonstrate. Illustrative examples are included to demonstrate the validity and applicability of the technique.
1

117
140


Parisa
Rahimkhani
Alzahra University
Alzahra University
I. R. Iran
p.rahimkhani@alzahra.ac.ir


Yadollah
Ordokhani
Alzahra University
Alzahra University
I. R. Iran
ordokhani2000@yahoo.com


Esmail
Babolian
KharazmiUniversity
KharazmiUniversity
I. R. Iran
babolian@khu.ac.ir
Fractionalorder Legendre wavelets
Fractional differential equations
Collocation method
Caputo derivative
Operational matrix
Solution of Troesch's problem through double exponential SincGalerkin method
2
2
SincGalerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the SincGalerkin approach were utilized to reduce the solution of nonlinear twopoint 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.
1

141
157


Mohammad
Nabati
Basic of Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadan, Iran
Basic of Sciences, Abadan Faculty of Petroleum
I. R. Iran
nabati@put.ac.ir


Mahdi
Jalalvand
Department of Mathematics, Faculty of Mathematical Sciences and Computer Shahid Chamran University, Ahvaz, Iran
Department of Mathematics, Faculty of Mathematical
Iran
m.jalalvand@scu.ac.ir
Sinc Function
Galerkin method
Double exponential transformation
Nonlinear Troesch's problem
BVP
Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
2
2
This article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multipoint 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 RiemannLiouville 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 classicalresults 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 applicabilityof our results, we provide some examples.
1

158
169


Kamal
Shah
University of Malakand
University of Malakand
Pakistan
kamalshah408@gmail.com


Salman
Zeb
Department of Mathematics university of Malakand
Department of Mathematics university of Malakand
Pakistan
salmanzeb@gmail.com


Rahmat
Khan
Dean of Science university of Malakand
Dean of Science university of Malakand
Pakistan
rahmat_alipk@yahoo.com
Fractional differential equations
Boundary value problems
Positive solutions
Green’s function
fixed point theorem
A wavelet method for stochastic Volterra integral equations and its application to general stock model
2
2
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.
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170
188


Saeed
Vahdati
Esfahan University
Esfahan University
Iran
sdvahdati@gmail.com
Wavelets
Brownian Motion
Stochastic integral equation
Stochastic differential equation
Ito integral