## Convergence of Adomian’s method applied to nonlinear equations.(English)Zbl 0822.65027

The nonlinear equation $$f(x)= 0$$ in $$\mathbb{R}$$ is transformed into the form $$x= F(x)+ c$$ ($$F$$ is a nonlinear function, $$c$$ is constant). The solution of the latter is calculated in the series form $$x= \sum^ \infty_{i= 0} x_ i$$ and $$F(x)= \sum^ \infty_{i= 0} A_ i$$, where $$A_ i$$’s are Adomian polynomials. The authors derive the convergence conditions and give the numerical examples.
Reviewer: A.Roose (Tallinn)

### MSC:

 65H05 Numerical computation of solutions to single equations
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### References:

 [1] Adomian, G., Nonlinear Stochastic Systems and Applications to Physics (1989), Kluwer · Zbl 0698.35099 [2] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer · Zbl 0802.65122 [3] Cherruault, Y.; Adomian, G., Decomposition method: A new proof of convergence, Math. Comput. Modelling, 18, 12, 103-106 (1993) · Zbl 0805.65057 [4] Adomian, G.; Rach, R., Algebraic computation and the decomposition method, Kybernetes, 15, 33-37 (1986) · Zbl 0604.60064 [5] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Mathl. Comput. Modelling, 28, 5, 103-110 (1994) · Zbl 0809.65073
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