Abstract

The existence and uniqueness solution of the Cauchy problem are discussed and proved in a Banach space E due to Bielecki method and Picard method depending on the properties we expect a solution to possess . Moreover , some properties concerning the stability of solution are obtained . The product Nyström method is used as a numerical method to obtain a linear system of algebraic equations. Also , many important theorems related to the existence and uniqueness solution of the algebraic system are derived . Finally , an application is given and numerical results are obtained.