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Abstract Abstract Many fields and some phenomena in engineering and the physical sciences require describing their behaviors by finding their governing equations (ordinary or integral) equations. Some of these fields include fluid dynamics (ocean motion), heat transfer, and modelling the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules. The solutions to those equations represent describing the behavior of a phenomenon or model this requires finding computational methods. The Adomian Decomposition Method is considered one of the most efficient semi-analytical methods. The aim of the thesis is to present a new modification of Adomian decomposition method which used Accelerated polynomials (El-Kalla polynomials) in solving non-linear integro-differential equations. We introduce a new modification of Laplace Adomian Decomposition Method based on El-Kalla polynomials. Some numerical examples are be presented to show the accuracy of our proposed method in solving this type. |