الفهرس 
Chapter - 1Only 14 pages are availabe for public view
 |  | from | 16 |  |  |
| | | from | 16 | | |
Abstract
Five chapters are discussed and developed for many NLODEs, based on the homo-
topy perturbation Sumudu transform method and Runge-Kutta fourth order method for
solving some real life problem which presented by ordinary di¤erential equations. Such
as, MSEIR, SHYP, SEIR, SIR, and SI models.
In this thesis, an approximate formula of the Caputo fractional derivatives using
Sumudu transform method are presented. We use these formula to nd a numerical
solution for the mentioned problems.
In chapter two, we introduce an approximate formula of the Caputo fractional deriv-
ative using the Sumudu transform method and implement this formula to obtain the
numerical solutions of some models which presented by FDEs such as SIR and SI models
mentioned in our gures.
In chapter three, by using the de nitions of Sumudu transform method on Caputo
derivatives, we implement this formula to obtain the numerical solutions for systems
have more equations of FDEs such as, MSEIR and SHYP models mentioned in our
gures.
In chapter four, we present a Runge-Kutta fourth method for solving systems of non-
linear di¤erential equations such as SIR and SI nonlinear di¤erential equations and the
results are shown in tables. The minimum error in the results is of the order e5 and it
increases up to e8 for SI and SIR models, it can be reduced by reducing step size by
using matlap program.
In chapter ve, by using the mentioned method in chapter four, we apply Runge-
Kutta fourth order on systems have more equations such as SEIR and MESIR nonlinear
ordinary di¤erential equations and the results are shown in tables. The minimum error
in the results is of the order e3 and it increases up to e6 for SEIR and MSEIR models,
9
it can be reduced by reducing step size by using matlap program.
In this thesis, from the previous results, we nd that the Sumudu transform method is
easier and faster in nding the solutions, but Runge-Kutta fourth order method is more
accurate in its results.