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Original Articles

Exponential spline method for approximation solution of Fredholm integro-differential equation

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Pages 791-801 | Received 27 Jun 2018, Accepted 18 Feb 2019, Published online: 17 Mar 2019

References

  • M. Amirfakhrian and K. Shakibi, Solving integro-differential equation by using b-spline interpolation, Int. J. Math. Model. Comput. 3(3) (2013), pp. 237–244.
  • M.A. Balci and M. Sezer, A Numerical approach based on exponential polynomials for solving of Fredholm integro-differential-difference equations, NTMSCI 3(2) (2015), pp. 44–54.
  • B. Basirat and M.A. Shahdadi, Numerical solution of nonlinear integro-differential equations with initial conditions by Bernstein operational matrix of derivative, Int. J. Modern Nonlinear Theor. Appl. 2 (2013), pp. 141–149. doi: 10.4236/ijmnta.2013.22018
  • S.H. Behiry, Solution of nonlinear Fredholm integro-differential equations using a hybrid of block pulse functions and normalized Bernstein polynomials, J. Comput. Appl. Math. 260 (2014), pp. 258–265. doi: 10.1016/j.cam.2013.09.036
  • S.H. Behiry and H. Hashish, Wavelet methods for the numerical solution of Fredholm integro-differential equations, Int. J. Appl. Math. 11(1) (2002), pp. 27–35.
  • S.H. Behiry and S.I. Mohamed, Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method, Nat. Sci. 4(8) (2012), pp. 581–587.
  • A. Belloura, D. Sbibih, and A. Zidna, Two cubic spline methods for solving Fredholm integral equations, Appl. Math. Comput. 276 (2016), pp. 1–11.
  • A.H. Bhrawy, E. Tohidi, and F. Soleymani, A new Bernoulii matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Appl. Math. Comput. 219 (2012), pp. 482–497.
  • H. Brunner, On the numerical solution of Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal. 27(4) (1990), pp. 87–96. doi: 10.1137/0727057
  • J. Chen, Y. Huang, H. Rong, T. Wu, and T. Zeng, A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation, J. Comput. Appl. Math. 290 (2015), pp. 633–640. doi: 10.1016/j.cam.2015.06.020
  • M. Dehghan and A. Saadatmandi, Chebyshev finite difference method for Fredholm integro-differential equation, Int. J. Comput. Math. 85 (2008), pp. 123–130. doi: 10.1080/00207160701405436
  • H. Derili Gherjalar and H. Mohammadikia, Numerical solution of functional integral and integro-differential equations by using b-splines, Appl. Math. (Irvine) 3 (2012), pp. 1940–1944. doi: 10.4236/am.2012.312265
  • M. El-Mikkawy and A. Karawia, Inversion of general tridiagonal matrices, Appl. Math. Lett. 19 (2006), pp. 715–720. doi: 10.1016/j.aml.2005.11.012
  • M. Feng and H. Pang, A class of three point boundary value problems for second-order impulsive integro-differential equations in Banach space, J. Nonlinear Anal. 70 (2009), pp. 64–82. doi: 10.1016/j.na.2007.11.033
  • R. Firouzdor, A. Heidarnejad Khoob, and Z. Mollaramezani, Numerical solution of functional integral equations by using B-splines, J. Linear Topol. Algebra 1(1) (2012), pp. 45–53.
  • Z. Mahmoodi, J. Rashidinia, and E. Babolian, B-Spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations, Appl. Anal. 93 (2013), pp. 1787–1802. doi: 10.1080/00036811.2012.702209
  • F. Mirzaee, Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials, Comput. Methods Differ. Equ. 5(2) (2017), pp. 88–102.
  • A.N. Netravali, Spline approximation to the solution of the Volterra integral equation of the second kind, Math. Comput. 27(121) (1973), pp. 99–106. doi: 10.1090/S0025-5718-1973-0366068-8
  • O.M. Ogunlaran and M.O. Oke, A numerical approach for solving first order integro-differential equations, Am. J. Comput. Appl. Math. 3(4) (2013), pp. 214–219.
  • Y. Ordokhani, An application of Walsh functions for Fredholm-Hammerstein integro-differential equations, Int. J. Contemp. Math. Sci. 5(22) (2010), pp. 1055–1063.
  • A. Saadatmandi and M. Dehghan, Numerical solution of high-order linear Fredholm integro-differential-difference equation with variable coefficients, Comput. Math. Appl. 59 (2010), pp. 2996–3004. doi: 10.1016/j.camwa.2010.02.018
  • P. Singh, S.D. Joshi, R.K. Patney, and K. Saha, Some studies on nonpolynomial interpolation and error analysis, Appl. Math. Comput. 244 (2014), pp. 809–821.
  • I.H. Sloan, Nonpolynomial interpolation, J. Approx. Theory 39 (1983), pp. 97–117. doi: 10.1016/0021-9045(83)90085-0
  • J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd ed. Springer Verlag, New York, 1992.
  • H.R Thiem, A model for spatio spread of an epidemic, J. Math. Bio. 4 (1977), pp. 337–351. doi: 10.1007/BF00275082
  • Z. Wang, L. Liu, and Y. Wu, The unique solution of boundary value problems for nonlinear second-order integro-differential equations of mixed type in Banach space, Comput. Math. Appl. 54 (2007), pp. 1293–1301. doi: 10.1016/j.camwa.2007.04.018
  • S. Yalcinbas, Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput. 127 (2002), pp. 195–206.
  • X. Yang and J. Shen, Periodic boundary value problems for second-order impulsive integro-differential equations, J. Comput. Appl. Math. 209 (2007), pp. 176–186. doi: 10.1016/j.cam.2006.10.082
  • S. Yeganeh, Y. Ordokhani, and A. Saadatmandi, A Sinc-collocation method for second-order boundary value problems of nonlinear integro-differential equation, J. Inf. Comput. Sci. 7(2) (2012), pp. 151–160.
  • W. Yulan, T. Chaolu, and P. Jing, New algorithm for second-order boundary value problems of integro-differential equation, J. Comput. Appl. Math. 229 (2009), pp. 1–6. doi: 10.1016/j.cam.2008.10.007
  • Ş. Yüzbaşi, An exponential collocation method for the solutions of the HIV infection model of CD4+T cells, Int. J. Biomath. 9(1650036) (2016), pp. 1650036-1–1650036-15.
  • Ş. Yüzbaşi, An exponential method to solve linear Fredholm-Volterra integro-differential equations and residual improvement, Turk. J. Math. 42 (2018), pp. 2546–2562. doi: 10.3906/mat-1707-66
  • Ş. Yüzbaşi and M. Karaçayir, An exponential Galerkin method for solutions of HIV Infection model of CD4+ T-cells, Comput. Biol. Chem. 67 (2017), pp. 205–212. doi: 10.1016/j.compbiolchem.2016.12.006
  • Ş. Yüzbaşi and M. Sezer, An exponential approximation for solutions of generalized pantograph-delay differential equations, Appl. Math. Model. 37 (2013), pp. 9160–9173. doi: 10.1016/j.apm.2013.04.028
  • Ş. Yüzbaşi and M. Sezer, An exponential matrix method for solving systems of linear differential equations, Math. Meth. Appl. Sci. 37 (2013), pp. 336–348. doi: 10.1002/mma.2593
  • Ş. Yüzbaşi and M. Sezer, Exponential collocation method for solutions of singularly perturbed delay differential equations, Abstr. Appl. Anal. (2013), pp. 1–10. doi:10.1155/2013/493204.
  • Ş. Yüzbaşi and M. Sezer, An exponential approximation for solutions of generalized pantograph-delay differential equations, Neural Comput. Appl. 27 (2016), pp. 769–779. doi: 10.1007/s00521-015-1895-y

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