The decomposition method for ordinary differential equations with discontinuities. (English) Zbl 1030.34012

Casasús, Luis; Al-Hayani, Waleed

Appl. Math. Comput. 131, No. 2-3, 245-251 (2002).

MSC:

34A45	Theoretical approximation of solutions to ordinary differential equations
34A36	Discontinuous ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

References:

[1]	Adomian, G., Stochastic Systems (1983), Academic Press: Academic Press New York · Zbl 0504.60067
[2]	Adomian, G., Nonlinear Stochastic Operator Equations (1986), Academic Press: Academic Press New York · Zbl 0614.35013
[3]	Adomian, G., Nonlinear Stochastic Systems Theory and Applications to Physics (1989), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0659.93003
[4]	Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0802.65122
[5]	Cabada, A.; Pouso, R. L.; Liz, E., A generalization of the method of upper and lower solutions for discontinuous first order problems with nonlinear boundary conditions, Appl. Math. Comput., 114, 135-148 (2000) · Zbl 1027.34006
[6]	Cabada, A.; Liz, E., Discontinuous impulsive differential equations with nonlinear boundary conditions, Nonlinear Anal., 28, 1491-1497 (1997) · Zbl 0878.34009
[7]	Heikkilä, S.; Cabada, A., On first order discontinuous differential equations with nonlinear boundary conditions, Nonlinear World, 3, 487-503 (1996) · Zbl 0895.34006
[8]	Heikkilä, S.; Lakshmikantham, V., Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations (1994), Marcel Dekker: Marcel Dekker New York · Zbl 0804.34001
[9]	Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Math. Comput. Modelling, 28, 5, 103-109 (1994) · Zbl 0809.65073
[10]	Abbaoui, K.; Cherruault, Y., New ideas for proving convergence of decomposition methods, Comput. Math. Appl., 29, 7, 103-108 (1995) · Zbl 0832.47051
[11]	Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to nonlinear equations, Math. Comput. Modelling, 20, 9, 60-73 (1994) · Zbl 0822.65027
[12]	Cherruault, Y.; Adomian, G., Decomposition methods: a new proof of convergence, Math. Comput. Modelling, 18, 12, 103-106 (1993) · Zbl 0805.65057
[13]	Guellal, S.; Cherruault, Y., Practical formula for calculation of Adomian’s polynomials and application to the convergence of the decomposition method, Internat. J. Bio-Medical Comput., 36, 223-228 (1994)
[14]	Wazwaz, A. M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput., 111, 53-69 (2000) · Zbl 1023.65108