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Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational tau method and error estimation. (English) Zbl 1170.65101

The authors investigate the solutions of a system of nonlinear Volterra integro-differential equations with an error estimation for a class using the operational tau method based on the paper of M. K. El-Daou and E. L. Ortiz [J. Math. Anal. Appl. 326, No. 1, 622–631 (2007; Zbl 1119.65065)].

MSC:

65R20 Numerical methods for integral equations
45G15 Systems of nonlinear integral equations
45J05 Integro-ordinary differential equations

Citations:

Zbl 1119.65065
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Full Text: DOI

References:

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[2] Ortiz, E. L., The Tau method, SIAM. J. Numer. Anal., 6, 480-492 (1969) · Zbl 0195.45701
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[6] Pour-Mahmoud, J.; Rahimi-Ardabili, M. Y.; Shahmorad, S., Numerical solution of the system of Fredholm integro-differential equations by the Tau method, Appl. Math. Comput., 168, 465-478 (2005) · Zbl 1082.65600
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[8] Ortiz, E. L., On the numerical solution of nonlinear and functional differential equations with the Tau method, (Numerical Treatment of Differential Equations in Applications. Numerical Treatment of Differential Equations in Applications, Lecture Notes in Mathematics, vol. 679 (1978), Springer-Verlag: Springer-Verlag Berlin), 127-139 · Zbl 0387.65053
[9] Ebadi, G.; Rahimi, M. Y.; Shahmorad, S., Numerical solution of the nonlinear Volterra integro-differential equations by the Tau method, Appl. Math. Comput., 188, 1580-1586 (2007) · Zbl 1119.65123
[10] Shahmorad, S., Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation, Appl. Math. Comput., 167, 1418-1429 (2005) · Zbl 1082.65602
[11] Hosseini, S. M.; Shahmorad, S., Numerical solution of a class of integro-differential equations by the Tau method with an error estimation, Appl. Math. Comput., 136, 550-570 (2003) · Zbl 1027.65182
[12] Dehghan, M.; Saadatmandi, A., A Tau method for the one-dimensional parabolic inverse problem subject to temperature overspecification, Comput. Math. Appl., 52, 933-940 (2006) · Zbl 1125.65340
[13] El-Daou, M. K.; Ortiz, E. L., The weighting subspaces of the Tau method and orthogonal collocation, J. Math. Anal. Appl., 326, 622-631 (2007) · Zbl 1119.65065
[14] Ebadi, G.; Rahimi-Ardabili, M. Y.; Shahmorad, S., Numerical solution of the system of nonlinear Fredholm integro-differential equations by the operational Tau method with an error estimation, Sci. Iran., 14, 6, 546-554 (2007) · Zbl 1178.65146
[15] J. Biazar, H. Ghazvini, M. Eslami, He’s homotopy perturbation method for systems of integro-differential equations, Chaos Solitons Fractals. doi:10.1016/j.chaos.2007.06.001; J. Biazar, H. Ghazvini, M. Eslami, He’s homotopy perturbation method for systems of integro-differential equations, Chaos Solitons Fractals. doi:10.1016/j.chaos.2007.06.001 · Zbl 1197.65106
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