The main themes of this thesis are oriented about studying and classifications of some inverse problems (in the differential and integral equations) with their numerical solutions. Also, one of the most important ideas in this work is to solve the direct and the inverse problems simultaneously. This study concern with the three methods, namely the forward method, the direct variational method and the least square method for solving some of the identifications problems in the (ordinary and partial) differential equations. For the inverse problems of the integral and integro-differential equations, we introduce a new method, namely the residual method as well as the direct variational method. To illustrate the methods described in this work, some examples are presented with some computer programs and the results are given in a tabular forms.