Applying the adomian mechanism to solve generalized non-linear initial value problems of fourth-order

This paper proposes a new creative modification to the well-known standard Adomian decomposition method (ADM) in order to investigate various types of initial-value problems (IVPs) involving distinct kinds of fourth order ordinary differential equations (ODEs). We demonstrate that the singular point at x=0, therefore the form factor, could show up in several equations terms. Some non-linear numerical applications that have been studied and explained this method have confirmed its effectiveness and ability to find appropriate solutions for such equations. The outcomes we arrive at with this operator are reliable and converge faster than the exact solution.