Adomian decomposition method for a class of nonlinear problems. (English) Zbl 1238.65086

Summary: The Adomian decomposition method together with some properties of nested integrals is used to provide a solution to a class of nonlinear ordinary differential equations and a coupled system.


65L99 Numerical methods for ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
Full Text: DOI


[1] Laraqi, N.; Rashidi, M. M.; Garcia de Maria, J. M.; Baïri, A., Analytical model for the thermohydrodynamic behaviour of a thin lubricant film, Tribology International, 44, 9, 1083-1086 (2011) · doi:10.1016/j.triboint.2011.04.012
[2] Laraqi, N.; Rashidi, M. M.; Garcia de Maria, J. M.; Baïri, A., Thermo-hydrodynamic behaviour of a thin lubricant film, Proceedings of the 3rd International Conference on Thermal Issues in Emerging Technologies Theory and Applications (ThETA ’10)
[3] Vintrou, S.; Laraqi, N.; Baïri, A., Thermal impedance of multi-finger microelectronic structures: exact analytical model, Journal of Physics D, 42, 24 (2009) · doi:10.1088/0022-3727/42/24/245501
[4] Laraqi, N.; Alilat, N.; de Maria, J. M. G.; Baïri, A., Temperature and division of heat in a pin-on-disc frictional device-Exact analytical solution, Wear, 266, 7-8, 765-770 (2009) · doi:10.1016/j.wear.2008.08.016
[5] Bauzin, J. G.; Laraqi, N.; Baïri, A., Estimation of thermal contact parameters at the interface of two sliding bodies, Journal of Physics: Conference Series, 135, 1 (2008) · doi:10.1088/1742-6596/135/1/012015
[6] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method. Solving Frontier Problems of Physics: The Decomposition Method, Fundamental Theories of Physics, 60, xiv+352 (1994), Dordrecht, The Netherlands: Kluwer Academic, Dordrecht, The Netherlands · Zbl 0802.65122
[7] Azreg-Aïnou, M., A developed new algorithm for evaluating Adomian polynomials, CMES. Computer Modeling in Engineering & Sciences, 42, 1, 1-18 (2009) · Zbl 1357.65067
[8] Wazwaz, A.-M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Applied Mathematics and Computation, 111, 1, 53-69 (2000) · Zbl 1023.65108 · doi:10.1016/S0096-3003(99)00047-8
[9] Chilov, G. E., Fonctions de Plusieurs Variables Réelles (1975), Moscow, Russia: Mir, Moscow, Russia · Zbl 0317.26011
[10] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to nonlinear equations, Mathematical and Computer Modelling, 20, 9, 69-73 (1994) · Zbl 0822.65027 · doi:10.1016/0895-7177(94)00163-4
[11] Wazwaz, A.-M., Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Applied Mathematics and Computation, 123, 1, 109-122 (2001) · Zbl 1027.35019 · doi:10.1016/S0096-3003(00)00064-3
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