2010
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1
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55
WELL POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS
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2
1

107
131


Allaberen
Ashyralyev
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University,
Turkey
aashyralyev@fatih.edu.tr


Ayfer
Dural
Gaziosman Paşa Lisesi Istanbul, Turkey
Gaziosman Paşa Lisesi Istanbul, Turkey
Turkey


Yaşar
Sözen
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University,
Turkey
ysozen@fatih.edu.tr
A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA
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2
Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.
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132
140


Victor
Plotnikov
Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
Department of Optimal Control and Economic
Ukraine


Olga
Kichmarenko
Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
Department of Optimal Control and Economic
Ukraine
olga.kichmarenko@gmail.com
averaging method
DIFFERENTIAL EQUATIONS WITH DELAY
DIFFERENTIAL EQUATIONS WITH MAXIMA
AUTOMATIC REGULATION
COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
2
2
In this paper, we present a comparative study between the Adomian decomposition method and two classical wellknown RungeKutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
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141
150


A. R.
Vahidi
Department of Mathematics, ShahreRey Branch, Islamic Azad University
Department of Mathematics, ShahreRey Branch,
Iran
alrevahidi@yahoo.com


GH.
Asadi Cordshooli
Department of Physics, ShahreRey Branch, Islamic Azad University
Department of Physics, ShahreRey Branch,
Iran


Z.
Azimzadeh
Department of Mathematics, Science and Research Branch, Islamic Azad University
Department of Mathematics, Science and Research
Iran
Adomian decomposition method
Differential equation
damped forced oscillator
[[1] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer, Dordrecht, 1989. ##[2] Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Dordrecht, 1994. ##[3] Yee E., Application of the decomposition method to the solution of the reaction convectiondiffusion equation, App. Math. And Computation, 56, 127, 1993. ##[4] ElSayed S. M., The modified decomposition method for solving non linear algebraic equations, App. Math. And Computation, 132, 589597, 2002. ##[5] Babolian E. and Biazar J., Solving the Problem of Biological Species Living Together by Adomian Decomposition Method, App. Math. And Computation 129, 339 343, 2002. ##[6] Babolian E. and Biazar J., Solving Concrete Examples by Adomian Method, App. Math. And Computation, 135, 161167, 2003. ##[7] Babolian E., Vahidi A. R. and Asadi Cordshooli G., Solving differential equations by decomposition Method, App. Math. And Computation, 167, 11501155, 2005. ##[8] Wazwaz A. M., The modified decomposition method and Pade approximations for solving Thomas Fermi equations, App. Math. And Computation, 105, 1119, 1999. ##[9] Wazwaz A. M., A comparison between Adomian decomposition method and Taylor series method in the series solution, App. Math. And Computation, 97, 3744, 1998. ##[10] Rach R., On the Adomian decomposition method and comparison with Picard's method, J. Math. Anal. Appl., 128 , 480483,1987. ##[11] Edwards J. T., Roberts J. A., Ford, N. J., A comparison of Adomian's decomposition method and Runge Kutta methods for approximate solution of some predator prey model equation, Numerical Analysis Report, No. 309, 1997. ##[12] ElSayed S. M., AbdolAziz M. R., A comparison of Adomian's decomposition method and waveletGalerkin method for solving integrodifferential equations, App. Math. And Computation, 136, 151159, 2003. ##[13] Bellomo N., and Sarafyan D., On a Comparison between Adomian's Decomposision Method and Picard Iteration, J. Math. Anal. Applic., No. 123, 1987. ##[14] Babolian E., Biazar J., and Vahidi A., On the decomposition method for system of linear equations and system of linear Volterra integral equations, App. Math. Comput., 147, 1927, 2004. ##[15] Goldstein H., Cassical mechanics, AddisonWesley, Massachusetts, 1980. ##[16] Thomsen J. J., Vibrations and stability order and chaos, McgrawHill, London, 1997. ##[17] Bhat Rama B., and Dukkipati V., Advanced dynamics, Alpha Science, Pangbourne, 2001. ##[18] Simmons G. F., Differential equations with applications and historical notes, Mcgraw Hill, London, 1972. ##[19] Cherruault Y., Convergence of Adomian's method, Kybernets, 18(2), 3139, 1989. ##[20] Cherruault Y., Some new results for convergence of Adomian's method applied to integral equations, Matl. Comput. Modeling, 16(2), 8593, 1992. ##[21] Adomian G., A review of the Decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501544, 1988. ##[22] Burden R. L., Dauglas Faires J., Numreical Analysis, Seventh Edition, Brooks/Cole, 2001. ##]
INTEGRATING CASEBASED REASONING, KNOWLEDGEBASED APPROACH AND TSP ALGORITHM FOR MINIMUM TOUR FINDING
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2
Imagine you have traveled to an unfamiliar city. Before you start your daily tour around the city, you need to know a good route. In Network Theory (NT), this is the traveling salesman problem (TSP). A dynamic programming algorithm is often used for solving this problem. However, when the road network of the city is very complicated and dense, which is usually the case, it will take too long for the algorithm to find the shortest path. Furthermore, in reality, things are not as simple as those stated in AT. For instance, the cost of travel for the same part of the city at different times may not be the same. In this project, we have integrated TSP algorithm with AI knowledgebased approach and casebased reasoning in solving the problem. With this integration, knowledge about the geographical information and past cases are used to help TSP algorithm in finding a solution. This approach dramatically reduces the computation time required for minimum tour finding.
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151
161


Hossein
Erfani
Department of computer Lahijan I.A.U.
Department of computer Lahijan I.A.U.
Iran
herfani@gmail.com
CASEBASED REASONING
KNOWLEDGEBASED APPROACH
Traveling salesman problem
CASEBASED TOUR FINDER
KNOWLEDGEBASED ROUTE FINDER
GEOGRAPHICAL INFORMATION