The defining stage of the process of solving ill-posed inverse problems is the choice of the regularization parameter

Comparison of the method of model experiments and the generalized residual principle

№
1	Average absolute	4,725	7,305	39,746	38,478
2	Average relative	0,207	0,383	0,989	0,992
3	Maximum absolute	12,040	17,970	91,118	80,655
4	Maximum relative	0,633	1,713	1,000	1,000

Fig. 3. Exact solution (1), (2) — solution obtained by model experiments, (3) — solution obtained by the generalized residual principle

In table 1 is the solution obtained by the method of model experiments; is the solution obtained by the generalized residual principle; is the exact solution. A comparison of the results obtained by the method of model experiments and the generalized residual principle indicates the effectiveness of using the method of model experiments for solving nonlinear integral equations of the first kind. From the table above it can be seen that in this example, the accuracy of the model experiment method is 1.5–2.7 times higher than the accuracy of the generalized residual principle.

Conclusion
The use of a combination of the Tikhonov method and the method of model experiments made it possible to obtain a specific numerical algorithm for solving nonlinear integral equations of the Fredholm type of the first kind and allows one to find an effective solution for problems with rapidly changing sections of the sought solutions.