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Ghomanjani, F.; Kılıçman, A.; Effati, S.

Numerical solution for IVP in Volterra type linear integrodifferential equations system. (English) Zbl 1291.65380

Abstr. Appl. Anal. 2013, Article ID 490689, 4 p. (2013).
Summary: A method is proposed to determine the numerical solution of system of linear Volterra integrodifferential equations (IDEs) by using Bezier curves. The Bezier curves are chosen as piecewise polynomials of degree \(n\), and Bezier curves are determined on \([t_0,t_f]\) by \(n+1\) control points. The efficiency and applicability of the presented method are illustrated by some numerical examples.

Cited in 7 Documents

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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\textit{F. Ghomanjani} et al., Abstr. Appl. Anal. 2013, Article ID 490689, 4 p. (2013; Zbl 1291.65380)
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References:

[1] Bo, T. L.; Xie, L.; Zheng, X. J., Numerical approach to wind ripple in desert, International Journal of Nonlinear Sciences and Numerical Simulation, 8, 2, 223-228 (2007)
[2] Xu, L.; He, J. H.; Liu, Y., Electro spun nano-porous spheres with Chinese drug, International Journal of Nonlinear Sciences and Numerical Simulation, 8, 2, 199-202 (2007)
[3] Agarwal, R.; O’Regan, D., Integral and integro-differential equations theory, methods and applications, 2 (2000), Singapore: The Gordon and breach science publishers, Singapore
[4] Rashidinia, J.; Tahmasebi, A., Taylor series method for the system of linear Volterra integro-differential equations, The Journal of Mathematics and Computer Science, 4, 3, 331-343 (2012)
[5] Maleknejad, K.; Mirzaee, F.; Abbasbandy, S., Solving linear integro-differential equations system by using rationalized Haar functions method, Applied Mathematics and Computation, 155, 2, 317-328 (2004) · Zbl 1056.65144
[6] Maleknejad, K.; Tavassoli Kajani, M., Solving linear integro-differential equation system by Galerkin methods with hydrid functions, Applied Mathematics and Computation, 159, 3, 603-612 (2004) · Zbl 1063.65145
[7] Yusufoğlu, E., An efficient algorithm for solving integro-differential equations system, Applied Mathematics and Computation, 192, 1, 51-55 (2007) · Zbl 1193.65234
[8] Saberi-Nadjafi, J.; Tamamgar, M., The variational iteration method: a highly promising method for solving the system of integro-differential equations, Computers & Mathematics with Applications, 56, 2, 346-351 (2008) · Zbl 1155.65399
[9] Arikoglu, A.; Ozkol, I., Solutions of integral and integro-differential equation systems by using differential transform method, Computers & Mathematics with Applications, 56, 9, 2411-2417 (2008) · Zbl 1165.45300
[10] Biazar, J.; Ghazvini, H.; Eslami, M., He’s homotopy perturbation method for systems of integro-differential equations, Chaos, Solitons & Fractals, 39, 3, 1253-1258 (2009) · Zbl 1197.65106
[11] Yusufoğlu, E., Numerical solving initial value problem for Fredholm type linear integro-differential equation system, Journal of the Franklin Institute, 346, 6, 636-649 (2009) · Zbl 1168.45300
[12] Biazar, J.; Eslami, M., Modified HPM for solving systems of Volterra integral equations of the second kind, Journal of King Saud University, 23, 1, 35-39 (2011)
[13] Huang, Y.; Li, X.-F., Approximate solution of a class of linear integro-differential equations by Taylor expansion method, International Journal of Computer Mathematics, 87, 6, 1277-1288 (2010) · Zbl 1191.65179
[14] Karamete, A.; Sezer, M., A Taylor collocation method for the solution of linear integro-differential equations, International Journal of Computer Mathematics, 79, 9, 987-1000 (2002) · Zbl 1006.65144
[15] Tahmasbi, A.; Fard, O. S., Numerical solution of linear Volterra integral equations system of the second kind, Applied Mathematics and Computation, 201, 1-2, 547-552 (2008) · Zbl 1148.65101
[16] Ghomanjani, F.; Farahi, M. H., The Bezier control points method for solving delay differential equation, Intelligent Control and Automation, 3, 2, 188-196 (2012)
[17] Zheng, J.; Sederberg, T. W.; Johnson, R. W., Least squares methods for solving differential equations using Bézier control points, Applied Numerical Mathematics, 48, 2, 237-252 (2004) · Zbl 1048.65077
[18] Ghomanjani, F.; Farahi, M. H.; Gachpazan, M., Bézier control points method to solve constrained quadratic optimal control of time varying linear systems, Computational & Applied Mathematics, 31, 3, 433-456 (2012) · Zbl 1259.49053
[19] Berenguer, M. I.; Garralda-Guillem, A. I.; Ruiz Galn, M., An approximation method for solving systems of Volterra integro-differential equations, Applied Numerical Mathematics, 67, 126-135 (2013) · Zbl 1266.65207
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