ORIGINAL_ARTICLE
WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS
http://ijo.iaurasht.ac.ir/article_513242_b696c46c223d5893189894ebd386e2a2.pdf
2009-04-01T11:23:20
2019-04-20T11:23:20
107
131
Allaberen
Ashyralyev
aashyralyev@fatih.edu.tr
true
1
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
AUTHOR
Ayfer
Dural
true
2
Gaziosman Paşa Lisesi Istanbul, Turkey
Gaziosman Paşa Lisesi Istanbul, Turkey
Gaziosman Paşa Lisesi Istanbul, Turkey
AUTHOR
Yaşar
Sözen
ysozen@fatih.edu.tr
true
3
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
Department of Mathematics, Fatih University, Istanbul,34500, Turkey
LEAD_AUTHOR
ORIGINAL_ARTICLE
A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA
Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.
http://ijo.iaurasht.ac.ir/article_513243_5f3c8ae8ea9dc142b1dc6d4d96b4a7fb.pdf
2009-07-01T11:23:20
2019-04-20T11:23:20
132
140
averaging method
DIFFERENTIAL EQUATIONS WITH DELAY
DIFFERENTIAL EQUATIONS WITH MAXIMA
AUTOMATIC REGULATION
Victor
Plotnikov
true
1
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 Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
AUTHOR
Olga
Kichmarenko
olga.kichmarenko@gmail.com
true
2
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 Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine
LEAD_AUTHOR
ORIGINAL_ARTICLE
COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta 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.
http://ijo.iaurasht.ac.ir/article_513244_30c8e012f97a5925f518417591ecc74f.pdf
2009-07-01T11:23:20
2019-04-20T11:23:20
141
150
Adomian decomposition method
Differential equation
damped forced oscillator
A. R.
Vahidi
alrevahidi@yahoo.com
true
1
Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University
Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University
Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University
LEAD_AUTHOR
GH.
Asadi Cordshooli
true
2
Department of Physics, Shahr-e-Rey Branch, Islamic Azad University
Department of Physics, Shahr-e-Rey Branch, Islamic Azad University
Department of Physics, Shahr-e-Rey Branch, Islamic Azad University
AUTHOR
Z.
Azimzadeh
true
3
Department of Mathematics, Science and Research Branch, Islamic Azad University
Department of Mathematics, Science and Research Branch, Islamic Azad University
Department of Mathematics, Science and Research Branch, Islamic Azad University
AUTHOR
[1] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer, Dordrecht, 1989.
1
[2] Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Dordrecht, 1994.
2
[3] Yee E., Application of the decomposition method to the solution of the reaction- convection-diffusion equation, App. Math. And Computation, 56, 1-27, 1993.
3
[4] El-Sayed S. M., The modified decomposition method for solving non linear algebraic equations, App. Math. And Computation, 132, 589-597, 2002.
4
[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.
5
[6] Babolian E. and Biazar J., Solving Concrete Examples by Adomian Method, App. Math. And Computation, 135, 161-167, 2003.
6
[7] Babolian E., Vahidi A. R. and Asadi Cordshooli G., Solving differential equations by decomposition Method, App. Math. And Computation, 167, 1150-1155, 2005.
7
[8] Wazwaz A. M., The modified decomposition method and Pade approximations for solving Thomas Fermi equations, App. Math. And Computation, 105, 11-19, 1999.
8
[9] Wazwaz A. M., A comparison between Adomian decomposition method and Taylor series method in the series solution, App. Math. And Computation, 97, 37-44, 1998.
9
[10] Rach R., On the Adomian decomposition method and comparison with Picard's method, J. Math. Anal. Appl., 128 , 480-483,1987.
10
[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.
11
[12] El-Sayed S. M., Abdol-Aziz M. R., A comparison of Adomian's decomposition method and wavelet-Galerkin method for solving integro-differential equations, App. Math. And Computation, 136, 151-159, 2003.
12
[13] Bellomo N., and Sarafyan D., On a Comparison between Adomian's Decomposision Method and Picard Iteration, J. Math. Anal. Applic., No. 123, 1987.
13
[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, 19-27, 2004.
14
[15] Goldstein H., Cassical mechanics, Addison-Wesley, Massachusetts, 1980.
15
[16] Thomsen J. J., Vibrations and stability order and chaos, Mcgraw-Hill, London, 1997.
16
[17] Bhat Rama B., and Dukkipati V., Advanced dynamics, Alpha Science, Pangbourne, 2001.
17
[18] Simmons G. F., Differential equations with applications and historical notes, Mcgraw- Hill, London, 1972.
18
[19] Cherruault Y., Convergence of Adomian's method, Kybernets, 18(2), 31-39, 1989.
19
[20] Cherruault Y., Some new results for convergence of Adomian's method applied to integral equations, Matl. Comput. Modeling, 16(2), 85-93, 1992.
20
[21] Adomian G., A review of the Decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501-544, 1988.
21
[22] Burden R. L., Dauglas Faires J., Numreical Analysis, Seventh Edition, Brooks/Cole, 2001.
22
ORIGINAL_ARTICLE
INTEGRATING CASE-BASED REASONING, KNOWLEDGE-BASED APPROACH AND TSP ALGORITHM FOR MINIMUM TOUR FINDING
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 knowledge-based approach and case-based 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.
http://ijo.iaurasht.ac.ir/article_513245_3c4d2bff5986f79d2b7094d0cd0a9317.pdf
2009-07-01T11:23:20
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151
161
CASE-BASED REASONING
KNOWLEDGE-BASED APPROACH
Traveling salesman problem
CASE-BASED TOUR FINDER
KNOWLEDGE-BASED ROUTE FINDER
Geographical Information
Hossein
Erfani
herfani@gmail.com
true
1
Department of computer Lahijan I.A.U.
Department of computer Lahijan I.A.U.
Department of computer Lahijan I.A.U.
LEAD_AUTHOR