A RELIABLE AND FAST ALGORITHM FOR FOURTH ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract
This work includes the extension of optimal homotopy asymptotic method to fourth-order Volterra integro-differential equations. This method converges more rapidly than any homotopy based method. Reliability of the method relates with the convergence. Convergence of the solution is controlled by convergence control parameters in the auxiliary function. Numerical results show excellent accuracy and efficiency of the proposed algorithm.
Keywords: Volterra integro-differential equations, optimal homotopy asymptotic method, auxiliary function, nonlinear problems.
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L.G. Chambers, Integral Equations, A Short Course, International Textbook Company, London, (1976).MATHGoogle Scholar
R.F. Churchhouse, Handbook of Applicable Mathematics, Wiley, New York, (1981).Google Scholar
B.L. Moiseiwitsch, Integral Equations, Longman, London and New York, (1977).MATHGoogle Scholar
V. Volterra, Theory of Functionals of Integral and Integro-Differential Equations, Dover, New York, (1959).MATHGoogle Scholar
R. P. Agarwal, Boundary value problems for higher order integro-differential equations, Nonlinear Analysis, Theory, Meth. Appl., 7, pp. 259-270, (1983)
J. Morchalo, On two point boundary value problem for integro-differential equation of second order, Fasc. Math., 9, pp. 51-56, (1975),
J. Morchalo, On two point boundary value problem for integro-differential equation of higher order, Fasc. Math., 9, pp. 77-96, (1975)
A. Wazwaz, A reliable algorithm for solving boundary value problems for higher-
order integro-differential equations, Appl. Math. Comp., 118, pp. 327-342, (2001).
V. Marinca, N.Herisanu, I. Nemes, Optimal homotopy asymptotic method with application to thin film flow, Cent. Eur. J. Phys., 6(3)(2008)648-653.
N.Herisanu, V. Marinca, T.Dordea,G.Madescu,A new analytical approach to nonlinear vibration of an electric machine, Proce. Romanian. Acad. 9(3)(2008).
V. Marinca, N. Herisanu, C. Bota, B.Marinca, An optimal homotopy asymptotic method applied to the steady flow of fourth-grade fluid past a porous plate,Appl.Math.Lett.22(2),(2009)245-251.
V. Marinca, N. Herisanu, An optimal homotopy asymptotic method for solving
Nonlinear equations arising in heat transfer, Int. Comm. Heat and Mass Transfer,5(2008)710-715.
Javed Ali, S.Islam, Siraj-UL-Islam, Gulzaman, The Solution of Multi Point Boundary Value Problems by the Optimal Homotopy Asymptotic Method, Volume 59, Issue 6, March 2010, Pages 2000-2006, Computer and Mathematics with Application.
Javed Ali, Saeed Islam, Hamid Khan, Gul Zaman, Solution of a Parameterized Sixth-Order Boundary Value Problem by the Optimal Homotopy Asymptotic Method, Volume 12 , Number 3/2011, pp. 167–172, Proceedings of the Romanian Academy, Series A.
Javed Ali, S. Islam, M. Tariq Rahim and Gul Zaman, Solution of Special Twelfth-Order Boundary value Problems by the Optimal Homotopy Asymptotic Method, 11 (3): 371-378, 2010, World Applied Science Journal(WASJ).
Javed Ali , S.Islam, Hamid Khan, Syed Inayat Ali Shah, Application of Optimal Homotopy Asymptotic Method to higher order boundary value problems, Volume 2012, Article ID 401217, 14 pages, doi:10.1155/2012/401217, Abstract and Applied Analysis.
Javed Ali , S.Islam, Syed Inayat Ali Shah , Hamid Khan, Application of Optimal Homotopy Asymptotic Method to 5th & 6th order boundary value problems, Volume 15(8):1120-1126, 2011, World Applied Science Journal(WASJ).
Hamid Khan, S. Islam, Javed Ali, and Inayat Ali Shah, A Comparison of different analytic solution to squeezing flow with slip boundary conditions, Volume 2012, Article ID 835268, 18 pages doi:10.1155/2012/835268. Abstract and Applied Analysis.