NUMERICAL METHODS FOR SOLVING THE EMDEN-FOWLER EQUATION - Alhaj, Wameed Mohammad (An-Najah National University, 2025)
Zhou was the first to present the differential transform method (DTM) in 1986 for the purpose of solving electrical circuit analysis problems including linear and nonlinear initially values [1]. Later, the differential equations were numerically solved using the DTM. This technique, which is based on Taylor series expansion but in another manner, allows for the rapid and correct solution of complex mathematical models by transforming a given differential equation into a set of algebraic equations. In this investigation, using this technique, we solve ordinary differential equations that are both linear and nonlinear. George Adomian devised and introduced the Adomian decomposition method (ADM) in [2-3], and it has been extensively discussed in the literature. We applied this technique to a wide range of ordinary differential equations, including both linear and nonlinear ones. The method was found to be strong, efficient, and capable of handling a large class of ordinary equations. The decomposition approach offers a number of noteworthy benefits because it shows quick convergence of the solution. The majority of ordinary differential equation types that arise in various physical models and scientific applications will be satisfactorily handled by the approach presented in this text. The technique addresses the problem immediately and straightforwardly, without the need for any limiting assumptions that could change the real behavior of the model in question. Also, the Emden-Fowler equation's solution applying DTM and the ADM is studied [4]. Both approaches are used to get approximations of the equation's solutions, demonstrating how well they work for nonlinear differential equations. According to the results, DTM and ADM have the ability to accurately solve complicated equations such as the Emden-Fowler equation.
طرق عددية لحل معادلة إمدن فولر