###### Abstract
This, of course, does not exclude the need to create a mathematical model (MM) of the processes under study as a perfect mechanism for a calculation experiment, but it allows significantly reduction of the number of necessary calculations without significantly losing the quality of the obtained result. Multiplicative models are widely used to process the results of calculation experiments (obtaining the function \(F=f(x_{i})\)). However, the problem of choosing a multiplier that precedes the product of functions has not been fully clarified. This multiplier is also called the coefficient of ignorance, and the evaluation of the obtained data depends on its choice. Initially, the multiplier was chosen as a function of independent parameters from the domain. It turned out that despite the high accuracy and significant costs for conducting the experiment, the quality function of the process had satisfactory accuracy only around the reference point. Attempts to determine the quality function at other points did not yield a positive result, despite the use of various multiplier selection algorithms [3]. It became clear that an experiment carried out at a point simply cannot satisfy the accuracy of the definition of the quality function at other points and should not be a function of coordinates, but a number for each point in the domain. On the other hand, any research process that is conducted using experiments, simulations, or mathematical models can be represented as a black box (Figure 1). Any process that can be represented in the form of a black box model can be applied to the method of successive approximation (SAP) used in this paper. Unlike many methods with a similar name, it does not use any derivatives of functions, which makes it attractive for use in a wide range of tasks. The black box model may be represented here by physical devices, systems of differential equations, mathematical formulas, and computer programs or application software packages (ASPs) that implement it. The results of research using the MM, as a rule, represent matrices of numbers or tables of numerical data. Functions are reproduced using their values on the parameter grid. The finer the mesh of a model, the more accurate approximations of the function are achievable. For complex problems, obtaining the values of functions on the parameters mesh requires significant expenditure of machine time, which makes the problem of reproduction of functions practically impossible. Therefore, the idea of using the method of obtaining MM according to a simplified procedure arose. According to this approach, the MM is obtained not on the parameters mesh, but at a certain point of the area of their definition. The algorithm proposed by the author of [4] makes it possible to significantly reduce the computational costs of reproducing the quality function, but only in the vicinity of a certain point. Thus, instead of calculating the values of the function on the parameter mesh, they are calculated only on the coordinate lines, which significantly reduces the number of calculations of the resulting function (Figure 2). The method of successive approximation (MSA) is a method that can be used in all fields from physical calculation to statistic and computer technology. It is possible to build an efficient and flexible computational method by using MSA [5]. This may be applied to the study of the fixed-point problems in the more abstract setting of Banach spaces (e.g., differential and integral equations, dynamical systems) [6]. The efficiency of such a method was also proven by comparing it to a variation iteration method under equivalent conditions [7]. MSA allows representation of functions in an analytical form (namely, in the form of a product of functions, each of which depends on one variable) when their values exist in  
Figure 1: Model of a black box: \(X(x_{1},x_{2},\ldots x_{n})\), control parameters or model variables.