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2013 | 219 | 12 | 6750-6760
Tytuł artykułu

Numerical solution of fractional integro-differential equations by a hybrid collocation method

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Fractional integro-differential equations have been recently solved by many methods, such as Adomian decomposition method, differential transform method, collocation method and Taylor expansion approach. In this paper a hybrid collocation method is used which combines a non-polynomial collocation used on the first subinterval and graded piecewise polynomial collocation used on the rest of the interval. A theoretical analysis for the convergence order of the method is presented. Some numerical examples are given which confirm the theoretical results.
Rocznik
Tom
219
Numer
12
Strony
6750-6760
Opis fizyczny
Bibliografia
  • 1. Arikoglu, A.& Ozkol, I., "Solution of fractional integro-differential equations by using fractional differential transform method", Chaos Solitons Fract., vol. 40, 2009, p.521-529
  • 2. Bagley, R.L.& Trovik, P.J., "A theoretical basis for the application of fractional calculus to viscoelasticity", J. Rheol., vol. 27, 1983, p.201-210
  • 3. Bonilla, B.& Rivero, M.& Trujillo, J.J., "On systems of linear fractional differential equations with constant coefficients", Appl. Math. Comput., vol. 187, 2007, p.68-78
  • 4. Brunner, H.& Pedas, A.& Vainikko, G., "The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations", Math. Comput., vol. 68, 1999, p.1079-1095
  • 5. Brunner, H., "Nonpolynomial spline collocation for Volterra equations with weakly singular kernels", SIAM J. Numer. Anal., vol. 20, 1983, p.1106-1119
  • 6. Brunner, H., "The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes", Math. Comput., vol. 45, 1985, p.417-437
  • 7. Brunner, H., "Collocation Methods for Volterra Integral and Related Functional Differential Equations", 2004
  • 8. H. Brunner, P.J. van der Houwen, The Numerical Solution of Volterra Integral Equations, CWI Monographs, vol. 3, Amsterdam, 1986.
  • 9. Cao, Y.& Herdman, T.& Xu, Y., "A hybrid collocation method for Volterra integral equations with weakly singular kernels", SIAM J. Numer. Anal., vol. 41, 2003, p.364-381
  • 10. Diethelm, K.& Ford, N.J.& Freed, A.D., "Deailed error analysis for a fractional Adams method", Numer. Algorithms, vol. 36, 2004, p.31-52
  • 11. Diethelm, K.& Ford, N.J.& Freed, A.D., "A predictor–corrector approach for the numerical solution of fractional differential equations", Nonlinear Dyn., vol. 29, 2002, p.3-22
  • 12. Goodrich, C.S., "Existence of a positive solution to a system of discrete fractional boundary value problems", Appl. Math. Comput., vol. 217, 2011, p.4740-4753
  • 13. Huang, L.& Li, X.F.& Zhao, Y.L.& Duan, X.Y., "Approximate solution of fractional integro-differential equations by Taylor expansion method", Comput. Math. Appl., vol. 62, 2011, p.1127-1134
  • 14. Jafari, H.& Gejji, V.D., "Solving a system of nonlinear fractional differential equations using Adomain decomposition", Appl. Math. Comput., vol. 196, 2006, p.644-651
  • 15. Jafari, H.& Gejji, V.D., "Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations", Appl. Math. Comput., vol. 181, 2006, p.598-608
  • 16. Lin, R.& Liu, F., "Fractional high order methods for the nonlinear fractional ordinary differential equation", Nonlinear Dyn., vol. 66, 2007, p.856-869
  • 17. Miller, K.S.& Ross, B., "An Introduction to the Fractional Calculus and Fractional Differential Equations", 1993
  • 18. Momani, S.& Al-Khaled, "Numerical solutions for systems of fractional differential equations by the decomposition method", Appl. Math. Comput., vol. 162, 2005, p.1351-1365
  • 19. Momani, S.& Hadid, S., "Lyapunov stability solutions of fractional integro-differential equations", Int. J. Math. Math. Sci., vol. 47, 2004, p.2503-2507
  • 20. Momani, S., "Local and global existence theorems on fractional integro-differential equations", J. Fract. Calc., vol. 18, 2000, p.81-86
  • 21. Momani, S., "Some existence theorems on fractional integro-differential equations", Abhath Al-Yarmouk J., vol. 10:2B, 2001, p.435-444
  • 22. Momani, S.& El-Khazali, R., "On the existence of extremal solutions of the fractional integro-differential equations", J. Fract. Calc., vol. 18, 2000, p.87-92
  • 23. Momani, S.& Noor, M.A., "Numerical methods for fourth order fractional integro-differential equations", Appl. Math.Comput., vol. 182, 2006, p.754-760
  • 24. Momani, S.& Qaralleh, A., "An efficient method for solving systems of fractional integro-differential equations", Comput. Math. Appl., vol. 52, 2006, p.459-470
  • 25. Nazaria, D.& Shahmorad, S., "Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions", J. Comput. Appl. Math., vol. 234, 2010, p.883-891
  • 26. Odibat, Z., "Analytic study on linear systems of fractional differential equations", Comput. Math. Appl., vol. 59, 2010, p.1171-1183
  • 27. Oldham, K.B.& Spanier, J., "The Fractional Calculus", Mathematics in Science and Engineering, vol. vol. 111, 1974
  • 28. Podlubny, I., "Fractional Differential Equations", Mathematics in Science and Engineering, vol. vol. 198, 1999
  • 29. Rawashdeh, E.A., "Numerical solution of fractional integro-differential equations by collocation method", Appl. Math. Comput., vol. 176, 2006, p.1-6
  • 30. Rebelo, M.& Diogo, T., "A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel", J. Comput. Appl. Math., vol. 234, 2010, p.2859-2869
  • 31. Saeedi, H.& Mohseni Moghadam, M., "Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets", Commun. Nonlinear. Sci. Numer. Simul., vol. 16, 2011, p.1216-1226
  • 32. Salem, H.A.H., "On the existence of continuous solutions for a singular system of non-linear fractional differential equations", Appl. Math. Comput., vol. 198, 2008, p.445-452
  • 33. te Riele, H.J.J., "Collocation methods for weakly singular second kind Volterra integral equations with non-smooth solution", IMA J. Numer. Anal., vol. 2, 1982, p.437-449
  • 34. Zhang, X.Y., "Some results of linear fractional order time-delay system", Appl. Math. Comput., vol. 197, 2008, p.407-411
  • 35. Zurigat, M.& Momani, S.& Odibat, Z.& Alawneh, A., "The homotopy analysis method for handling systems of fractional differential equations", Appl. Math. Model., vol. 34, 2010, p.24-35
Typ dokumentu
Bibliografia
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