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Original Articles

Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials

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Pages 2100-2111 | Received 08 Mar 2016, Accepted 21 Jul 2017, Published online: 23 Aug 2017

References

  • M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Wiley, New York, 1972.
  • O. Abu Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integro differential equations, Neural Comput. Appl. 28 (2015), pp. 1591–1610. doi: 10.1007/s00521-015-2110-x
  • O. Abu Arqub, M. AL-Smadi, S. Momani, and T. Hayat, Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method, Soft Comput. 20(8) (2016), pp. 3283–3302. doi: 10.1007/s00500-015-1707-4
  • A. Akyuz-Dascioglu, A Chebyshev polynomial approach for linear Fredholm–Volterra integro-differential equations in the most general form, Appl. Math. Comput. 181 (2006), pp. 103–112.
  • A. Avudainayagam and C. Vani, Wavelet-Galerkin method for integro-differential equations, Appl. Numer. Math. 32 (2000), pp. 247–254. doi: 10.1016/S0168-9274(99)00026-4
  • A.H. Bhrawy, E. Tohidi, and F. Soleymani, A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Appl. Math. Comput. 219 (2012), pp. 482–497.
  • N.M. Chuong and N.V. Tuan, Spline collocation methods for Fredholm integro-differential equations of second order, Acta Math. Vietnam. 20(1) (1995), pp. 85–98.
  • N.M. Chuong and N.V. Tuan, Spline collocation methods for Fredholm–Volterra integro-differential equations of high order, Vietnam J. Math. 25(1) (1997), pp. 15–24.
  • P. Darania and A. Ebadian, A method for the numerical solution of the integro-differential equations, Appl. Math. Comput. 188 (2007), pp. 657–668.
  • M. Gulsu, B. Gurbuz, Y. Ozturk, and M. Sezer, Laguerre polynomial approach for solving linear delay difference equations, Appl. Math. Comput. 217 (2011), pp. 6765–6776.
  • S.M. Hosseini and S. Shahmorad, Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases, Appl. Math. Model. 27 (2003), pp. 145–154. doi: 10.1016/S0307-904X(02)00099-9
  • Z. Hu, Boundness of solutions to functional integro-differential equations, Proc. Amer. Math. Soc. 114(2) (1992), pp. 519–526. doi: 10.1090/S0002-9939-1992-1070520-3
  • R.P. Kanwal and K.C. Liu, A Taylor expansion approach for solving integral equations, Int. J. Math. Educ. Sci. Technol. 20(3) (1989), pp. 411–414. doi: 10.1080/0020739890200310
  • A. Karamete and M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79(9) (2002), pp. 987–1000. doi: 10.1080/00207160212116
  • K. Maleknejad and Y. Mahmoudi, Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions, Appl. Math. Comput. 149 (2004), pp. 799–806.
  • P. Natalini and A. Bernaridini, A generalization of the Bernoulli polynomials, J. Appl. Math. 3 (2003), pp. 155–163. doi: 10.1155/S1110757X03204101
  • B. Neta, Numerical solution of a nonlinear integro-differential equation, J. Math. Anal. Appl. 89 (1982), pp. 598–611. doi: 10.1016/0022-247X(82)90119-6
  • Y. Öztürk, A. Gülsu, and M. Gülsu, A numerical approach for solving modified epidemiological model for drug release systems, Nevşehir Bilim ve Teknoloji Dergisi 2(2) (2013), pp. 56–64.
  • Y. Öztürk, A. Gülsu, and M. Gülsu, A numerical method for solving the mathematical model of controlled drug release, Bitlis Eren Üniversitesi, Fen Bilimleri Dergisi 2(2) (2013), pp. 169–175.
  • Y. Öztürk, A. Gülsu, and M. Gülsu, On solution of a modified epidemiological model for drug release systems, Sch. J. Phys. Math. Stat. 3(1) (2016), pp. 1–5.
  • M. Sezer and M. Gulsu, Polynomial solution of the most general linear Fredholm integro-differential-difference equations by means of Taylor matrix method, Int. J. Complex Var. 50(5) (2005), pp. 367–382. doi: 10.1080/02781070500128354
  • M. Sezer and M. Gulsu, A new polynomial approach for solving difference and Fredholm integro-differential equation with mixed argument, Appl. Math. Comput. 171 (2005), pp. 332–344.
  • N.M. Temme, Special Functions in Mathematical Physics, Wiley – Interscience, New York, 1996.
  • E. Tohidi, A.H. Bhrawy, and K. Erfani, A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation, Appl. Math. Model. 37 (2013), pp. 4283–4294. doi: 10.1016/j.apm.2012.09.032
  • M. Turkyilmazoglu, An effective approach for numerical solutions of high-orderFredholm integro-differential equations, Appl. Math. Comput. 227 (2014), pp. 384–398.
  • S. Yalcinbaş and M. Sezer, The approximate solution of high-order linear Volterra–Fredholm integrodifferential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2002), pp. 291–308.

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