A new operational approach for numerical solution of generalized functional integro-differential equations.(English)Zbl 1325.65182

The authors present a computational method based on the operational Jacobi collocation method for solving generalized functional linear and nonlinear integro-differential equations with mixed argument. As examples, they also solve several functional integro-differential equations, using the proposed method.

MSC:

 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 45A05 Linear integral equations 45G10 Other nonlinear integral equations
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References:

 [1] Borhanifar, A.; Kabir, M. M., New periodic and soliton solutions by application of application of exp-function method for nonlinear evolution equation, Comput. Appl. Math., 229, 158-167, (2009) · Zbl 1166.65050 [2] Borhanifar, A.; Kabir, M. M.; Maryam Vahdat, L., New periodic and soliton wave solutions for the generalized Zakharov system and $$(2 + 1)$$-dimensional Nizhnik-Novikov-Veselov system, Chaos Solitons Fractals, 42, 1646-1654, (2009) · Zbl 1198.35216 [3] Borhanifar, A.; Zamiri, A., Application of $$(\frac{G^\prime}{G})$$-expansion method for the zhiber-Shabat equation and other related equations, Math. Comput. Modelling, 54, 2109-2116, (2011) · Zbl 1235.35236 [4] Borhanifar, A.; Abazari, R., Exact solutions for nonlinear schrodinger equations by differential transformation method, Appl. Math. Comput., 1-15, (2009) [5] Borhanifar, A.; Jafari, H.; Karimi, S. A., New solitary wave solutions for the bad Boussinesq and good Boussinesq equations, Numer. Methods Partial Differential Equations, 25, 1231-1237, (2009) · Zbl 1172.65380 [6] Yüzbaşı, Ş.; Sezer, M., An improved Bessel collocation method with a residual error function to solve a class of Lane-Emden differential equations, Math. Comput. Modelling, 57, 1298-1311, (2013) [7] Yüzbaşı, Ş.; Sezer, M., An exponential matrix method for solving systems of linear differential equations, Appl. Math. Comput. Sci., 36, 336-348, (2013) · Zbl 1261.65082 [8] Iserles, A.; Liu, Y. K., On pantograph integro-differential equations, J. Integral Equations Appl., 6, 213-237, (1994) · Zbl 0816.45005 [9] Ali, I., Convergence analysis of spectral methods for integro-differential equations with vanishing proportional delays, J. Comput. Math., 29, 49-60, (2011) · Zbl 1249.65281 [10] Brunner, H.; Hu, Q. Y., Optimal superconvergence results for delay integro-differential equations of pantograph type, SIAM J. Numer. Anal., 45, 986-1004, (2007) · Zbl 1144.65083 [11] Kolmanovskki, V.; Myshkis, A., Optimal superconvergence results for delay integro-differential equations of pantograph type, SIAM J. Numer. Anal., 45, 986-1004, (2007) · Zbl 1144.65083 [12] Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M., A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations, Appl. Numer. Math., 77, 43-54, (2014) · Zbl 1302.65175 [13] Wang, K.; Wang, Q., Taylor collocation method and convergence analysis for the Volterra-Fredholm integral equations, J. Comput. Appl. Math., 260, 294-300, (2014) · Zbl 1293.65174 [14] Wang, K.; Wang, Q., Lagrange collocation method for solving Volterra-Fredholm integral equation, Appl. Math. Comput., 219, 10434-10440, (2013) · Zbl 1304.65280 [15] Bhrawy, A.; Assas, L. M.; Tohidi, E.; Alghamdi, M. A., A Legendre-gauus collocation method for neutral functional-differential equations with proportional delays, Adv. Difference Equ., (2013) · Zbl 1380.65116 [16] Sezer, M.; Akyüz-Daşcloǧlu, A., A Taylor method for numerical solution of generalized pantograph equations with linear functional argument, J. Comput. Appl. Math., 200, 217-225, (2007) · Zbl 1112.34063 [17] Abazari, R.; Kılıcman, A., Application of differential transform method on nonlinear integro-differential equations with proportional delay, Neural Comput. Appl., 24, 391-397, (2014) [18] Erdem, K.; Yalçinbaş, S.; Sezer, M., A Bernoulli polynomial approach with residual correction for solving mixed linear Fredholm integro-differential-difference equations, J. Difference Equ. Appl., 19, 10, 1619-1631, (2013) · Zbl 1277.65114 [19] Kreyszig, E., Introduction functional analysis with applications, (1978), John Wiley and Sons, Inc. [20] Rashed, M. T., Numerical solution of functional differential, integral and integro-differential equations, Appl. Math. Comput., 156, 485-492, (2004) · Zbl 1061.65146
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