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Numerical solution of system of nonlinear second-order integro-differential equations. (English) Zbl 1201.65138

Summary: Numerical solution of a system of nonlinear second-order integro-differential equations with boundary conditions of the Fredholm and Volterra types by means of the Sinc-collocation method is considered. The method is effective for approximation in the case of the presence of end-point singularities. Properties of the Sinc-collocation method required for our subsequent development are given and utilized to reduce the computation of boundary value problems to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
45J05 Integro-ordinary differential equations
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[1] Linz, P., Analytical and Numerical Methods for Volterra Equations (1985), SIAM: SIAM Philadelphia, PA · Zbl 0566.65094
[2] Abdul Jerri, J., Introduction to Integral Equations with Applications (1999), John Wiley and Sons: John Wiley and Sons New York · Zbl 0938.45001
[3] Abbasbandy, S.; Taati, A., Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation, J. Comput. Appl. Math., 231, 106-113 (2009) · Zbl 1170.65101
[4] Khani, A.; Mohseni Moghadam, M.; Shahmorad, S., Numerical solution of special class of system of non-linear Volterra integro-differential equations by a simple high accuracy method, Bull. Iran. Math. Soc., 34, 2, 141-152 (2008) · Zbl 1168.65428
[5] Ebadi, G.; Rahimi, 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, 546-554 (2007) · Zbl 1178.65146
[6] Stenger, F., Numerical Methods Based on Sinc and Analytic Functions (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0803.65141
[7] Lund, J.; Bowers, K., Sinc Methods for Quadrature and Differential Equations (1992), SIAM: SIAM Philadelphia, PA · Zbl 0753.65081
[8] Eggert, N.; Jarratt, M.; Lund, J., Sinc function computations of the eigenvalues of Sturm-Lioville problems, J. Comput. Phys., 69, 209-229 (1987) · Zbl 0618.65073
[9] Lund, J.; Rilay, B. V., A Sinc-collocation method for the computation of the eigenvalues of the radial Schrodinger equation, IMA J. Numer. Anal., 4, 83-98 (1984) · Zbl 0544.65057
[10] Carlson, T. S.; Dockery, J.; Lund, J., A Sinc-collocation method for initial value problems, Math. Comp., 66, 215-235 (1997) · Zbl 0854.65054
[11] Al-Khaled, K., Sinc numerical solution for solitons and solitary waves, J. Comput. Appl. Math., 130, 283-292 (2001) · Zbl 1010.65043
[12] El-Gamel, M., Sinc and the numerical solution of fifth-order boundary value problems, Appl. Math. Comput., 187, 1417-1433 (2007) · Zbl 1121.65087
[13] Weber, V.; Daul, C.; Baltensperger, R., Radial numerical integrations based on the sinc function, Comput. Phys. Commun., 163, 133-142 (2004) · Zbl 1196.65056
[14] Koonprasert, S.; Bowers, K. L., Block matrix Sinc-Galerkin solution of the wind-driven current problem, Appl. Math. Comput., 155, 607-635 (2004) · Zbl 1126.65320
[15] Rashidinia, J.; Zarebnia, M., Solution of a Volterra integral equation by the Sinc-collocation method, J. Comput. Appl. Math., 206, 801-813 (2007) · Zbl 1120.65136
[16] Rashidinia, J.; Zarebnia, M., Convergence of approximate solution of system of Fredholm integral equations, J. Math. Anal. Appl., 333, 1216-1227 (2007) · Zbl 1120.65137
[17] Abdella, K.; Yu, X.; Kucuk, I., Application of the Sinc method to a dynamic elasto-plastic problem, J. Comput. Appl. Math., 223, 626-645 (2009) · Zbl 1153.74051
[18] Stenger, F., Fourier series for zeta function via Sinc, Linear Algebra Appl., 429, 2636-2639 (2008) · Zbl 1149.42002
[19] Stenger, F., Polynomial function and derivative approximation of Sinc data, J. Complexity, 25, 292-302 (2009) · Zbl 1180.65028
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