ABSTRACT
This chapter describes the approximation method for finding the generalized solution of the problem without using its classic solution. It explores the justification of the mathematical models determination by the generalized method. The generalized solution of the problem is not necessarily its classic solution. However, the twice-differentiable generalized solution is the classic solution of the problem. The generalized solution of the problem is an element of the larger set than the classic one. The relation between the sequential and generalized states is an analogue of the generalized and classic states. The generalized solution has weaker functional properties than the classic one. Therefore, the proof of the solvability of the problem and the convergence of the numerical method for the generalized method are easier than the classic one. The classical form of the model is based on the direct description of the structure of the object, and the generalized one describes the response of the system to any external influence.
