Existence and approximation of solutions for systems of first order differential equations

The purpose of this paper is to present some general results concerning the existence of solutions for systems of differential equations. The existence results to be presented will be based on an effective procedure for constructing approximate solution. Namely, a numerical scheme using the Sinc function, in which it is shown that the solution converges exponentially. Furthermore, a numerical example and comparisons are presented to prove the validity of the suggested method.