ORIGINAL_ARTICLE
NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE
This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed method has eighth-order accuracy in spaceand fourth-order accuracy in time variables. From the computational pointof view, the solution obtained by this method is in excellent agreement withthose obtained by previous works and also it is ecient to use. Numericalexamples are given to show the applicability and eciency of the method.
http://ijm2c.iauctb.ac.ir/article_521901_936793ccd67aa883ea91bb8556e0da36.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
291
305
Dierential Equation
Quintic Spline
Heat Equation
Wave Equation
Taylor Approximation
Jalil
Rashidinia
true
1
Department of Mathematics, Iran University of Science and Technology,
Iran, Islamic Republic of
Department of Mathematics, Iran University of Science and Technology,
Iran, Islamic Republic of
Department of Mathematics, Iran University of Science and Technology,
Iran, Islamic Republic of
AUTHOR
Mohamadreza
Mohsenyzade
true
2
AUTHOR
ORIGINAL_ARTICLE
LIMITED GROWTH PREY MODEL AND PREDATOR MODEL USING HARVESTING
In this paper, we have proposed a study on controllability and optimal harvestingof a prey predator model and mathematical non linear formation of the equation equilibriumpoint of Routh harvest stability analysis. The problem of determining the optimal harvestpolicy is solved by invoking Pontryagin0s maximum principle dynamic optimization of theharvest policy is studied by taking the combined harvest eect as a dynamics variable
http://ijm2c.iauctb.ac.ir/article_521902_9a677f0d5a98a73da478146fb8484dbb.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
307
318
Predator prey model
harvesting
Stability
optimal harvest policy
equilibrium point
Pontryagins maximum principle
Vijaya Rekha
Rekha
true
1
http://www.annamalaiuniversity.ac.in
Department of mathematics,Annamalai university
India
Assistant professor, Department of Mathematics, Annamalai university.
http://www.annamalaiuniversity.ac.in
Department of mathematics,Annamalai university
India
Assistant professor, Department of Mathematics, Annamalai university.
http://www.annamalaiuniversity.ac.in
Department of mathematics,Annamalai university
India
Assistant professor, Department of Mathematics, Annamalai university.
AUTHOR
ORIGINAL_ARTICLE
SLIDING MODE CONTROL BASED ON FRACTIONAL ORDER CALCULUS FOR DC-DC CONVERTERS
The aim of this paper is to design a Fractional Order Sliding Mode Controllers (FOSMC)for a class of DC-DC converters such as boost and buck converters. Firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. Secondly, themathematical proof of the stability condition and convergence of the proposed fractionalorder sliding surface is presented. Finally the effectiveness and robustness of the proposed ap-proaches compared with classical SMCs are demonstrated by simulation results with differentcases.
http://ijm2c.iauctb.ac.ir/article_521903_6dcc0e7d8decb0f28ded6044741b77e4.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
319
333
DC-DC Buck converter
DC-DC Boost converter
fractional order calculus
FOSMC
Noureddine
Bouarroudj
true
1
Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de Développement des Energies Renouvelables, CDER, 47133 Ghardaïa, Algeria
Algeria
Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de Développement des Energies Renouvelables, CDER, 47133 Ghardaïa, Algeria
Algeria
Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de Développement des Energies Renouvelables, CDER, 47133 Ghardaïa, Algeria
Algeria
AUTHOR
D.
Boukhetala
true
2
AUTHOR
B.
Benlahbib
true
3
AUTHOR
B.
Batoun
true
4
AUTHOR
ORIGINAL_ARTICLE
ADOMIAN DECOMPOSITION METHOD AND PADÉ APPROXIMATION TO DETERMINE FIN EFFICIENCY OF CONVECTIVE SOLAR AIR COLLECTOR IN STRAIGHT FINS
In this paper, the nonlinear differential equation for the convection of the temperature distribution of a straight fin with the thermal conductivity depends on the temperature is solved using Adomian Decomposition Method and Padé approximation(PADM) for boundary problems. Actual results are then compared with results obtained previously using digital solution by Runge–Kuttamethod and a differential transformation method (DTM) in order toverify the accuracy of the proposed method.
http://ijm2c.iauctb.ac.ir/article_521904_c066f626b5622b5a31ac24f1d3990801.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
335
346
Fin efficiency
Thermal conductivity
Adomian Decomposition Method (ADM)
Differential TransformationMethod (DTM)
Numerical Solution (NS)
Tabet
Ismail
true
1
Algeria
Algeria
Algeria
AUTHOR
M.
Kezzar
true
2
AUTHOR
K.
Touafe
true
3
AUTHOR
N.
Bellel
true
4
AUTHOR
S.
Gherieb
true
5
AUTHOR
A.
Khelifa
true
6
AUTHOR
M.
Adouane
true
7
AUTHOR
ORIGINAL_ARTICLE
DYNAMIC COMPLEXITY OF A THREE SPECIES COMPETITIVE FOOD CHAIN MODEL WITH INTER AND INTRA SPECIFIC COMPETITIONS
The present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are established. Stability analysis including local and global stability of the equilibria has been carried out in order to examine the dynamic behaviour of the system. The present system experiences Hopf-Andronov bifurcation for suitable choice of parameter values. As a result, intra-specific competition among predator populations can be beneficial for the survival of predator. The ecological implications of both the analytical and numerical findings are discussed at length towards the end.
http://ijm2c.iauctb.ac.ir/article_521905_792a15353565c5b8329cab70652e91f6.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
347
360
food chain
Inter and intra-specific competition
Global stability
Hopf-Andronov bifurcations
Lyapunov function
N.
Ali
true
1
AUTHOR
Santabrata
Chakravarty
true
2
Visva-Bharati University
India
Visva-Bharati University
India
Visva-Bharati University
India
AUTHOR
ORIGINAL_ARTICLE
APPROXIMATION SOLUTION OF TWO-DIMENSIONAL LINEAR STOCHASTIC FREDHOLM INTEGRAL EQUATION BY APPLYING THE HAAR WAVELET
In this paper, we introduce an efficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.
http://ijm2c.iauctb.ac.ir/article_521906_7f235bc58a75400bffaa9e3923b2af38.pdf
2015-03-21T11:23:20
2020-04-10T11:23:20
361
372
Haar wavelet
Two-dimensional stochastic Fredholm integral equation
Brownian motion process
Morteza
Khodabin
true
1
Karaj Branch, Islamic Azad University
Iran, Islamic Republic of
Karaj Branch, Islamic Azad University
Iran, Islamic Republic of
Karaj Branch, Islamic Azad University
Iran, Islamic Republic of
AUTHOR
Khosrow
Maleknejad
true
2
Iran, Islamic Republic of
Iran, Islamic Republic of
Iran, Islamic Republic of
AUTHOR
Mohsen
Fallahpour
true
3
Iran, Islamic Republic of
Iran, Islamic Republic of
Iran, Islamic Republic of
AUTHOR
I. Aziz, Siraj-ul-Islam, F. Khan, A new method based on Haar wavelet for numerical solution of two-dimensional nonlinear integral equations, J. Comp. Appl. Math. 272 (2014), 70-80.
1
I. Aziz, Siraj-ul-Islam, New algorithms for numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comp. Appl. Math. 239 (2013) 333-345.
2
Siraj-ul-Islam, I. Aziz, M. Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, Int, J. Comp. Math. 90 (2013) 1971-1989.
3
Siraj-ul-Islam, I. Aziz, A. Al-Fhaid, An improved method based on Haar wavelets for numerical solution of nonlinear and integro-differential equations of rst and higher orders, J. Comp. Appl. Math. 260 (2014) 449-469.
4
Kuo, Hui-Hsiung, Introduction to stochastic integration, Springer Science+Business Media, Inc. 2006.
5
K. E. Atkinson, The numerical solution of integral equations of the second kind, Cambridge University Press (1997).
6
A. J. Jerri, Introduction to integral equations with applications, John Wiley and Sons, INC (1999).
7
T. S. Sankar, V. I. Fabrikant, Investigations of a two-dimentional integral equation in the theory of elasticity and electrostatics, J. Mec. Theor. Appl. 2 (1983) 285-299.
8
H. J. Dobner, Bounds for the solution of hyperbolic problems, Computing 38 (1987) 209-218.
9
V. M. Aleksandrov, A. V. Manzhirov, Two-dimentional integral equations in applied mechanics of deformable solids, J. Appl. Mech. Tech. Phys. 5 (1987) 146-152.
10
A. V. Manzhirov, Contact problems of the interaction between viscoelastic foundations subject to ageing and systems of stamps not applied simultaneously, Prikl. Matem. Mekhan. 4 (1987) 523-535.
11
O. V. Soloviev, Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity, Radiophysics and Quantum Electronics 41 (1998) 392-402.
12
M. Rahman, "A rigid elliptical disc-inclusion in an elastic solid", subject to a polynomial normal shift, J. Elasticity 66 (2002) 207-235.
13
H. Guoqiang, W. Jiong, Extrapolation of nystrom solution for two dimentional nonlinear Fredholm integral equations, J. Comp. App. Math. 134 (2001) 259-268.
14
H. Brunner, Collocation methods for Volterra integral and related functional equations, Cambridge University Press, 2004.
15
H. Guoqiang, K. Itayami, K. Sugihara, W. Jiong, Extrapolation method of iterated collocation solution for two-dimentional nonlinear Volterra integral equations, Appl. Math. Comput. 112 (2000) 49-61.
16
W. Xie, F. R. Lin, A fast numerical solution method for two dimensional Fredholm integral equations of the second kind, App. Num. Math. 59 (2009) 1709-1719.
17
S. Bazm, E. Babolian, Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Gauss product quadrature rules, Commun. Nonlinear Sci. Numer. Simult. 17 (2012) 1215-1223.
18
G. Han, R. Wang, Richardson extrapolation of iterated discrete Galerkin solution for two dimensional Fredholm integral equations, J. Comp. App. Math. 139 (2002) 49-63.
19
K. Maleknejad, Z. JafariBehbahani, Application of two-dimensional triangular functions for solving nonlinear class of mixed Volterra-Fredholm integral equations, Math. Comp. Mode. 55(2012) 1833-1844.
20
E. Babolian, K. Maleknejad, M. Roodaki, H. Almasieh, Two dimensional triangular functions and their applications to nonlinear 2d Volterra-Fredholm equations, Comp. Math. App. 60 (2010) 1711-1722.
21
S. Nemati, P. Lima, Y. Ordokhani, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using legender polynomials, J. Comp. Appl. Math. 242 (2013) 53-69.
22
A. Tari, M. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comp. Appl. Math. 228 (2009) 70-76.
23
P. Assari, H. Adibi, M. Dehghal, A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis, J. Comp. Appl. Math. 239 (2013) 72-92.
24
M. H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12-20.
25
F. Hosseini Shekarabi, K. Maleknejad, R. Ezzati, Application of two-dimensional Bernstein polynomials for solving mixed Volterra-Fredholm integral equations, African Mathematical Union and Springer-Verlag Berlin Heidelberg, DOI 10. 1007/s 13370-014-0283-6 2014.
26
F. Keinert, Wavelets and Multiwavelets, A Crc Press Company Boca Raton London New York Washington, D. C, 2004.
27