Optimization of the Adomian Decomposition Method for Solving Differential Equation with Fractional Order


Department of Mathematics, Shiraz University of Technology, Shiraz, Iran


Up to now, Adomian Decomposition Method (ADM) has been widely employed in solving different kinds of differential equations. However, in many cases it is observed that the ADM has a lower precision in comparison with other methods, especially that of Homotopic ones. ADM is a relatively general and powerful method for finding analytical approximate results from different equations. In this paper, we seek to raise Optimal Adomian Decomposition Method (OADM) precision by employing the standard pattern of ADM. The main character of this repetitive method is based on employment of a controlling parameter in convergence, which resemble the parameters used in Homotopy Analysis Method (HAM). This parameter is indicated in such a way to reasonably increase the precision of obtained results. To indicate the optimizing parameter, the Least Squares Method has been used. The presented examples demonstrate that,  how  the above mentioned method has validity, applicability and a high degree of precision in solving differential equations of  fractional order so that it can be generally used in solving differential equations.

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