ORIGINAL_ARTICLE
Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials
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.
http://cmde.tabrizu.ac.ir/article_5911_e0ade60b77cb2f95092df545478f04e8.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
88
102
Fredholm-Volterra integral equation
Bell polynomials
Collocation method
Operational matrix
Error analysis
Farshid
Mirzaee
f.mirzaee@malayeru.ac.ir
true
1
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
LEAD_AUTHOR
[1] E. Babolian and M. Mordad, A numerical method for solving system of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl., 62 (2011), 187-198.
1
[2] E. T. Bell, Exponential polynomials, Ann. of Math., 35 (1934), 258-277.
2
[3] A. Bernardini and P. E. Ricci, Bell polynomials and dierential equations of Freud-type polyno-mials, Math. Comput. Model., 36 (2002), 1115-1119.
3
[4] H. Brunner, On the numerical solution of Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal., 27(4) (1990), 87-96.
4
[5] C. A. Charalambides, Enumerative Combinatorics, Chapman and Hall/CRC, Boca Raton, 2002.
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[6] L. Comtet, Advanced Combinatorics: The art of nite and innite expansions, D. Reidel publishing co., Dordrecht, 1974.
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[7] L. M. Delves and J. L. Mohamed, Computational methods for integral equations, Cambridge University Press, Cambridge, 1985.
7
[8] A. Di Cave and P. E. Ricci, Suipolinomidi Bell edinumeridi Fibonacciedi Bernoulli [On Bell polynomials and Fibonacci and Bernoulli numbers], Le Matematiche., 35 (1980), 84-95.
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[9] M. Gasca and T. Sauer, On the history of multivariate polynomial interpolation, J Comput. Appl. Math., 122 (2000), 23-35.
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[10] M. Ghasemi, M. Tavassoli Kajani, and E. Babolian, Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput., 188 (2007), 446-449.
10
[11] F. A. Hendi and A. M. Albugami, Numerical solution for Fredholm-Volterra integral equation of the second kind by using collocation and galerkin methods, J. King Saud Uni., 22 (2010),37-40.
11
[12] M. G. Kendall and A. Stuart, The advanced theory of statistics, Grin, London, 1958.
12
[13] A. Kurosh, Coyrs d' Algebre Superieure, Editions Mir, Moscow, 1971.
13
[14] K. Maleknejad, H. Almasieh, and M. Roodaki, Triangular functions (TFs) method for the solution of nonlinear Volterra-Fredholm integral equations, Commun. Nonlin. Sci. Numer. Simula., 15 (2010), 3293-3298.
14
[15] J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003.
15
[16] F. Mirzaee and E. Hadadiyan, Numerical solution of Volterra-Fredholm integral equations via modication of hat functions, Appl. Math. Comput., 280 (2016), 110-123.
16
[17] Y. Ordokhani and M. Razzaghi, Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized haar functions, Appl. Math. Lett., 21 (2008), 4-9.
17
[18] J. Riordan, An introduction to combinatorial analysis, Wiley publication in mathematical statistics, John Wiley sons, New Yorks, 1958.
18
[19] W. Wang and T. Wang, General identities on Bell polynomials, Comput. Math. Appl., 58 (2009), 104-118.
19
[20] S. Yalcinbas, Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 127 (2002), 195-206.
20
[21] S. Yousefi and M. Razzaghi, Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations, Math. Comput. Simula., 70 (2005), 419-428.
21
ORIGINAL_ARTICLE
A new approach on studying the stability of evolutionary game dynamics for financial systems
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.
http://cmde.tabrizu.ac.ir/article_6011_94343d3d340300caa3f9b4216d2424ef.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
103
116
Heterogeneous Agent Model
Adaptive Belief System
Evolutionary Game Theory
Rational Agent
Evolutionary Stable Strategies
Narges
Talebi Motlagh
n.talebi@tabrizu.ac.ir
true
1
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
LEAD_AUTHOR
Amir
Rikhtegar Ghiasi
agiasi@tabrizu.ac.ir
true
2
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
AUTHOR
Farzad
Hashemzadeh
hashemzadeh@tabrizu.ac.ir
true
3
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
AUTHOR
Sehraneh
Ghaemi
ghaemi@tabrizu.ac.ir
true
4
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
Control Engineering Department,
Faculty of Electrical and Computer Engineering: University of Tabriz, Tabriz, Iran
AUTHOR
ORIGINAL_ARTICLE
Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions
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.
http://cmde.tabrizu.ac.ir/article_6012_41565e9da3ef7f1d50237b20695692e6.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
117
140
Fractional-order Legendre wavelets
Fractional differential equations
Collocation method
Caputo derivative
Operational matrix
Parisa
Rahimkhani
p.rahimkhani@alzahra.ac.ir
true
1
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
AUTHOR
Yadollah
Ordokhani
ordokhani2000@yahoo.com
true
2
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences,
Alzahra University, Tehran, Iran
LEAD_AUTHOR
Esmail
Babolian
babolian@khu.ac.ir
true
3
Department of Computer Science, Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
Department of Computer Science, Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
Department of Computer Science, Faculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
AUTHOR
ORIGINAL_ARTICLE
Solution of Troesch's problem through double exponential Sinc-Galerkin method
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.
http://cmde.tabrizu.ac.ir/article_6013_7f8f210d6d5b95f23cb319b0f61ae6b7.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
141
157
Sinc Function
Galerkin method
Double exponential transformation
Nonlinear Troesch's problem
BVP
Mohammad
Nabati
nabati@put.ac.ir
true
1
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering,
Petroleum University of Technology, Abadan, Iran
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering,
Petroleum University of Technology, Abadan, Iran
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering,
Petroleum University of Technology, Abadan, Iran
LEAD_AUTHOR
Mahdi
Jalalvand
m.jalalvand@scu.ac.ir
true
2
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
AUTHOR
ORIGINAL_ARTICLE
Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
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.
http://cmde.tabrizu.ac.ir/article_6077_786926df406ec4f5042d803915a6e8dd.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
158
169
Fractional differential equations
Boundary value problems
Positive solutions
Green’s function
fixed point theorem
Kamal
Shah
kamalshah408@gmail.com
true
1
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
LEAD_AUTHOR
Salman
Zeb
salmanzeb@gmail.com
true
2
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
AUTHOR
Rahmat Ali
Khan
rahmat_alipk@yahoo.com
true
3
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
AUTHOR
ORIGINAL_ARTICLE
A wavelet method for stochastic Volterra integral equations and its application to general stock model
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.
http://cmde.tabrizu.ac.ir/article_6086_e150ecd516bdd8b7471d970f4fdb80a1.pdf
2017-04-01T11:23:20
2018-02-21T11:23:20
170
188
Wavelets
Brownian Motion
Stochastic integral equation
Stochastic differential equation
Ito integral
Saeed
Vahdati
sdvahdati@gmail.com
true
1
Department of Mathematics,
Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
Department of Mathematics,
Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
Department of Mathematics,
Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
LEAD_AUTHOR