Using quadratic interpolation to accelerate the convergence of a continuous analog of the Newton method

The paper analyzes the change in the characteristics of the convergence of the Continuous analogue of the Newton's method (NAMN) with different behavior of the residual function in the process of applying the method to solve a nonlinear equation. The influence of iterative option in the NAMS on the area and speed of convergence. Based on the analysis, it was proposed to introduce additional conditions for the use of a number of modifications of the NAMN algorithm in accordance with the behavior of the residual. An approach to the optimization of THE namh convergence process based on the use of quadratic interpolation of approximate solutions obtained in previous iterations is proposed. A mechanism was developed to control the convergence characteristics of NAMN using a number of control parameters, such as the step change coefficient of the difference scheme for the numerical solution of the differential equation NAMN. On the basis of the developed mechanism of convergence process control, a modification of the continuous analogue of Newton's method is proposed.