Previous |  Up |  Next


Title: Approximation of solutions of the forced duffing equation with nonlocal discontinuous type integral boundary conditions (English)
Author: Alsaedi, Ahmed
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 44
Issue: 4
Year: 2008
Pages: 295-305
Summary lang: English
Category: math
Summary: A generalized quasilinearization technique is applied to obtain a sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with nonlocal discontinuous type integral boundary conditions. (English)
Keyword: duffing equation
Keyword: integral boundary conditions
Keyword: quasilinearization
Keyword: quadratic convergence
MSC: 34A45
MSC: 34B10
MSC: 34B15
idZBL: Zbl 1212.34017
idMR: MR2493426
Date available: 2009-01-29T09:15:29Z
Last updated: 2013-09-19
Stable URL:
Reference: [1] Ahmad, B.: A quasilinearization method for a class of integro-differential equations with mixed nonlinearities.Nonlinear Anal. Real World Appl. 7 (2006), 997–1004. Zbl 1111.45005, MR 2260894
Reference: [2] Ahmad, B., Alsaedi, A.: Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions.Nonlinear Anal. Real World Appl. 10 (2009), 358–367. Zbl 1154.34314, MR 2451715
Reference: [3] Ahmad, B., Alsaedi, A., Alghamdi, B.: Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions.Nonlinear Anal. Real World Appl. 9 (2008), 1727–1740. Zbl 1154.34311, MR 2422576
Reference: [4] Ahmad, B., Naz, U., Khan, R. A.: A higher order monotone iterative scheme for nonlinear Neumann boundary value problems.Bull. Korean Math. Soc. 42 (2005), 17–22. Zbl 1090.34510, MR 2122762, 10.4134/BKMS.2005.42.1.017
Reference: [5] Ahmad, B., Nieto, J. J.: The monotone iterative technique for three-point second-order integrodifferential boundary value problems with p-Laplacian.Boundary Value Problems 2007 (2007), 9pp., Article ID 57481, doi: 10.1155/2007/57481. Zbl 1149.65098, MR 2320689
Reference: [6] Ahmad, B., Nieto, J. J.: Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions.Nonlinear Anal. 69 (2008), 3291–3298. Zbl 1158.34049, MR 2450538
Reference: [7] Ahmad, B., Nieto, J. J., Shahzad, N.: The Bellman-Kalaba-Lakshmikantham quasilinearization method for Neumann problems.J. Math. Anal. Appl. 257 (2001), 356–363. MR 1827327, 10.1006/jmaa.2000.7352
Reference: [8] Ahmad, B., Sivasundaram, S.: The monotone iterative technique for impulsive hybrid set valued integro-differential equations.Nonlinear Anal. 65 (2006), 2260–2276. Zbl 1111.45006, MR 2267622, 10.1016/
Reference: [9] Bellman, R., Kalaba, R.: Quasilinearization and Nonlinear Boundary Value Problems.Amer. Elsevier, New York, 1965. Zbl 0139.10702, MR 0178571
Reference: [10] Bouziani, A., Benouar, N. E.: Mixed problem with integral conditions for a third order parabolic equation.Kobe J. Math. 15 (1998), 47–58. Zbl 0921.35068, MR 1654526
Reference: [11] Cabada, A., Nieto, J. J.: Rapid convergence of the iterative technique for first order initial value problems.Appl. Math. Comput. 87 (1997), 217–226. Zbl 0904.65067, MR 1468300, 10.1016/S0096-3003(96)00285-8
Reference: [12] Cannon, J. R.: Encyclopedia of Math. and its The one-dimensional heat equation, Addison-Wesley, Mento Park, CA, 1984. MR 0747979
Reference: [13] Cannon, J. R., Esteva, S. Perez, Hoek, J. Van Der: A Galerkin procedure for the diffusion equation subject to the specification of mass.SIAM. J. Numer. Anal. 24 (1987), 499–515. MR 0888747, 10.1137/0724036
Reference: [14] Choi, Y. S., Chan, K. Y.: A parabolic equation with nonlocal boundary conditions arising from electrochemistry.Nonlinear Anal. 18 (1992), 317–331. Zbl 0757.35031, MR 1150422, 10.1016/0362-546X(92)90148-8
Reference: [15] Denche, M., Marhoune, A. L.: Mixed problem with integral boundary condition for a high order mixed type partial differential equation.J. Appl. Math. Stoch. Anal. 16 (2003), 69–79. Zbl 1035.35085, MR 1973079, 10.1155/S1048953303000054
Reference: [16] Ewing, R. E., Lin, T.: A class of parameter estimation techniques for fluid flow in porous media.Adv. Water Res. 14 (1991), 89–97. MR 1108193, 10.1016/0309-1708(91)90055-S
Reference: [17] Formaggia, L., Nobile, F., Quarteroni, A., Veneziani, A.: Multiscale modelling of the circulatory system: a preliminary analysis.Comput. Vis. Sci. 2 (1999), 75–83. Zbl 1067.76624, 10.1007/s007910050030
Reference: [18] Ionkin, N. I.: Solution of a boundary value problem in heat condition with a nonclassical boundary condition.Differ. Uravn. 13 (1977), 294–304. MR 0603291
Reference: [19] Kartynnik, A. V.: Three-point boundary value problem with an integral space-variable condition for a second-order parabolic equation.Differential Equations 26 (1990), 1160–1166. Zbl 0729.35053, MR 1080432
Reference: [20] Ladde, G. S., Lakshmikantham, V., Vatsala, A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1985. Zbl 0658.35003, MR 0855240
Reference: [21] Lakshmikantham, V., Nieto, J. J.: Generalized quasilinearization for nonlinear first order ordinary differential equations.Nonlinear Times & Digest 2 (1995), 1–10. Zbl 0855.34013, MR 1333329
Reference: [22] Lakshmikantham, V., Vatsala, A. S.: Mathematics and its Applications, Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1998. MR 1640601
Reference: [23] Nieto, J. J., Rodriguez-Lopez, R.: Monotone method for first-order functional differential equations.Comput. Math. Appl. 52 (2006), 471–484. Zbl 1140.34406, MR 2263515, 10.1016/j.camwa.2006.01.012
Reference: [24] Shi, P.: Weak solution to evolution problem with a nonlocal constraint.SIAM J. Math. Anal. 24 (1993), 46–58. MR 1199526, 10.1137/0524004
Reference: [25] Vatsala, A. S., Yang, J.: Monotone iterative technique for semilinear elliptic systems.Boundary Value Probl. 2 (2005), 93–106. Zbl 1143.65388, MR 2198745
Reference: [26] Yurchuk, N. I.: Mixed problem with an integral condition for certain parabolic equations.Differential Equations 22 (1986), 1457–1463. Zbl 0654.35041, MR 0880769


Files Size Format View
ArchMathRetro_044-2008-4_5.pdf 436.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo