One of Wazwaz's significant contributions is the development of the (ADM). This method is a powerful tool for solving nonlinear integral equations. The ADM is based on the decomposition of the unknown function into a series of components, which are then solved recursively.

A signature of Wazwaz’s teaching style is the emphasis on modern "direct" and "reliable" computational schemes that often bypass the need for traditional transformation methods. Key methods include: National Academic Digital Library of Ethiopia Adomian Decomposition Method (ADM):

Wazwaz categorizes integral equations into two primary types based on the limits of integration:

: The unknown function appears both under the integral sign and as a derivative. Singular Equations : The kernel