Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation

Author

Zagazig University, Faculty of Science, Egypt

10.1016/j.joems.2015.01.001

Abstract

We study the two analytical methods, the classical method of successive approxima-
tions (Picard method), Adomian decomposition method (ADM) see (Abbaoui and Cherruault, 1994;
Adomian et al., 1992; Adomian, 1995) [1–3] and the (numerical method) predictor corrector method
(PECE) for an initial value problem of arbitrary (fractional) orders differential equation (FDE). The
existence and uniqueness of the solution will be proved and the convergence will be discussed for each
method. Some examples will be studied.

Keywords

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2
2016
Pages 165-170

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