zbMATH — the first resource for mathematics

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)
[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)
[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)
[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)
[6] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Fundamental Theories of Physics, 60, xiv+352, (1994), 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
[9] Chilov, G. E., Fonctions de Plusieurs Variables Réelles, (1975), Mir, Moscow, Russia
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.