Mahmoud, R. (2016). Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation. test, 24(2), 165-170. doi: 10.1016/j.joems.2015.01.001
R. A. Mahmoud. "Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation". test, 24, 2, 2016, 165-170. doi: 10.1016/j.joems.2015.01.001
Mahmoud, R. (2016). 'Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation', test, 24(2), pp. 165-170. doi: 10.1016/j.joems.2015.01.001
Mahmoud, R. Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation. test, 2016; 24(2): 165-170. doi: 10.1016/j.joems.2015.01.001

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

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2, 2016, Pages 165-170    PDF (332.28 K)
DOI: 10.1016/j.joems.2015.01.001
Author
R. A. Mahmoud
Zagazig University, Faculty of Science, Egypt
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
Fractional differential equation; Picard method; Adomian method; Predictor corrector method; Convergence analysis; Error analysis
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