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The decomposition method for stiff systems of ordinary differential equations. (English) Zbl 1082.65561
Summary: The decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases, focusing our interest in stiff problems.

65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L05Initial value problems for ODE (numerical methods)
34A30Linear ODE and systems, general
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Adomian, G.: Stochastic systems. (1983) · Zbl 0523.60056
[2] Adomian, G.: Nonlinear stochastic operator equations. (1986) · Zbl 0609.60072
[3] Adomian, G.: Nonlinear stochastic systems theory and applications to physics. (1989) · Zbl 0659.93003
[4] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[5] Bellomo, N.; Monaco, R. A.: Comparison between Adomian’s decomposition methods and perturbation techniques for nonlinear random differential equations. J. math. Anal. appl. 110, 495-502 (1985) · Zbl 0575.60064
[6] J.T. Edwards, J.A. Roberts, N.J. Ford, A comparison of Adomian’s decomposition method and Runge Kutta methods for approximate solution of some predator prey model equations, Numerical Analysis Report No. 309, The University of Manchester-UMIST, October 1997.
[7] Olek, S.: An accurate solution to the multispecies Lotka-Volterra equations. SIAM rev. 36, No. 3, 480-488 (1994) · Zbl 0802.92018
[8] Rach, R.: On the Adomian (decomposition) method and comparisons with Picard’s method. J. math. Anal. appl. 128, 480-483 (1987) · Zbl 0645.60067
[9] Shawgfeh, N. T.; Adomian, G.: Non-perturbative analytical solution of the general Lotka-Volterra three-species system. Appl. math. Comput. 76, 251-266 (1996) · Zbl 0846.65034
[10] Wazwaz, A. M.: A comparison between Adomian decomposition method and Taylor series method in the series solutions. Appl. math. Comput. 97, 37-44 (1998) · Zbl 0943.65084
[11] Abbaoui, K.; Cherruault, Y.: Convergence of Adomian’s method applied to differential equations. Math. comput. Modell. 28, No. 5, 103-109 (1994) · Zbl 0809.65073
[12] Abbaoui, K.; Cherruault, Y.: New ideas for proving convergence of decomposition methods. Comput. math. Appl. 29, No. 7, 103-108 (1995) · Zbl 0832.47051
[13] Abbaoui, K.; Cherruault, Y.: Convergence of Adomian’s method applied to nonlinear equations. Math. comput. Modell. 20, No. 9, 69-73 (1994) · Zbl 0822.65027
[14] Cherruault, Y.; Adomian, G.: Decomposition methods: a new proof of convergence. Math. comput. Modell. 18, No. 12, 103-106 (1993) · Zbl 0805.65057
[15] Guellal, S.; Cherruault, Y.: Practical formula for calculation of Adomian’s polynomials and application to the convergence of the decomposition method. Int. J. Bio-medical comput. 36, 223-228 (1994)
[16] Wu, X. -Y.; Xia, J. -L.: Two low accuracy methods for stiff systems. Appl. math. Comput. 123, 141-153 (2001) · Zbl 1024.65053
[17] A.C. Hindmarsh, G.D. Byrne, Applications of EPISODE: an experimental package for the integration of systems of ordinary differential equations, 1976.
[18] Hairer, E.; Wanner, G.: Solving ordinary differential equations II. (1991) · Zbl 0729.65051