Taylor Series Method for the System of Linear Volterra Integro-differential Equations
-
2737
Downloads
-
3853
Views
Authors
J. Rashidinia
- School of Mathematics, Iran University of Science and Technology, P. O. Box, 16846-13114, Tehran, Iran
A. Tahmasebi
- School of Mathematics, Iran University of Science and Technology, P. O. Box, 16846-13114, Tehran, Iran
Abstract
A method to determine the numerical solution of system of linear Volterra integro-differential equations
(IDEs) is proposed. The method obtains Taylor expansion for the exact solution of system of linear Volterra
IDEs at initial point \(x = 0\). In addition, we introduce a procedure to obtain an approximation for Taylor
expansion of the exact solution at \(x\neq 0\). Moreover, error estimation of the proposed methods is presented.
The efficiency and applicability of the presented methods is illustrated by some numerical examples.
Share and Cite
ISRP Style
J. Rashidinia, A. Tahmasebi, Taylor Series Method for the System of Linear Volterra Integro-differential Equations, Journal of Mathematics and Computer Science, 4 (2012), no. 3, 331--343
AMA Style
Rashidinia J., Tahmasebi A., Taylor Series Method for the System of Linear Volterra Integro-differential Equations. J Math Comput SCI-JM. (2012); 4(3):331--343
Chicago/Turabian Style
Rashidinia, J., Tahmasebi, A.. "Taylor Series Method for the System of Linear Volterra Integro-differential Equations." Journal of Mathematics and Computer Science, 4, no. 3 (2012): 331--343
Keywords
- system of linear Volterra integro-differential equations
- numerical solution
- Taylor expansion
- power series method
- integral equation.
MSC
References
-
[1]
T. L. Bo, L. Xie, X. J. Zheng, Numerical approach to wind ripple in desert, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 223--228
-
[2]
F. Z. Sun, M. Gao, S. H. Lei, Y. B. Zhao, K. Wang, Y. T. Shi, N. H. Wang, The fractal dimension of the fractal model of drop-wise condensation and its experimental study, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 211--222
-
[3]
H. Wang, H. M. Fu, H. F. Zhang, Z. Q. Hu, A practical thermodynamic method to calculate the best glass-forming composition for bulk metallic glasses, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 171--178
-
[4]
L. Xu, J. H. He, Y. Liu, Electrospun nanoporous spheres with Chinese drug, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 199--202
-
[5]
R. Agarwal, D. O’Regan, Integral and integro-differential equations theory, methods and applications, CRC Press, Singapore (2000)
-
[6]
K. Maleknejad, F. Mirzaee, S. Abbasbandy, Soling linear integro-differential equations system by using rationalized Haar functions method, Appl. Math. Comput., 155 (2004), 317--328
-
[7]
K. Maleknejad, M. Tavassoli Kajani, Solving linear integro-differential equation system by Galerkin methods with hybrid functions, Appl. Math. Comput., 159 (2004), 603--612
-
[8]
E. yusufoglu, An efficient algorithm for solving integro-differential equations system, Appl. Math. Comput., 192 (2007), 51--55
-
[9]
J. Sabri-Nadjafi, M. Tamamgar, The Variational iteration method: A highly promising method for solving the system of integro-differential equations, Computers & Mathematics with Applications, 56 (2008), 346--351
-
[10]
A. Arikoglu, I. Oskol, Solution of integral and integro-differential equation systems by using differential transform method, Computers & Mathematics with Applications, 56 (2008), 2411--2417
-
[11]
J. Biazar, H. Ghazevini, M. Eslami, He’s homotopy perturbation method for systems of integro-differential equations, Chaos Solitons Fractals, 39 (2009), 1253--1258
-
[12]
E. yusufoglu, Numerical solving initial value problem for Fredholm type linear integro-differential equation system, J. Franklin Inst., 346 (2009), 636--649
-
[13]
H. Aminikhah, A new analytical method for solving systems of linear integro-differential equations, Journal of King Saud University-Science, Vol. 23, 349--353, (2011)
-
[14]
Y. Huang, X. F. Li, Approximate solution of a class of linear integro-differential equations by Taylor expansion method, Int. J. Comput. Math., 87 (2010), 1277--1288
-
[15]
A. Karamete, M. Sezer, A Taylor Collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math., 79 (2002), 987--1000
-
[16]
A. Tahmasbi, O. S. Fard, Numerical solution of linear Volterra integral equations system of the second kind, Appl. Math. Comput., 201 (2008), 547--552
-
[17]
L. M. Delves, J. L. Mohamad, Computational method for integral equations, Cambrige University Press, Cambrige (1985)
-
[18]
M. I. Berenguer, A. I. Garralda-Guillem, M. Ruiz Galn, An approximation method for solving systems of Volterra integro-differential equations, Appl. Numer. Math., Vol. 67, 126--135, (2013)