### Speaker

Dmitrii Kazakov
(Dubna State University)

### Description

A mechanism for controlling the convergence of the continuous analog of the Newton method (NAMN) with the use, as a control parameter, of the step variation coefficient of the difference scheme for the numerical solution of the differential equation of the NAMN. Using the example of a developed algorithm for a modified NAMN, it was shown that it is possible to control the characteristics of the convergence of NAMN using the step change coefficient of the difference scheme for the numerical solution of the differential equation of the NAMN as a control parameter. The development and implementation of mechanisms for controlling the iterative processes of solving the equations will make it possible to significantly reduce the time required to calculate the required value, which will significantly improve the efficiency of the algorithms for solving nonlinear equations.
References
1.E.G. Nikonov. One class of conservative difference schemes for solving molecular dynamics equations of motion. arXiv:1605.05714v1 [math.NA].
2. Gavurin M.K. Nonlinear functional equations and continuous analogues of iterative methods [Text]: Izv. Higher education \ Gavurin M.K. - Mat., No. 5, 18-31 (1958).
3. T. Zhanlav, I. V. Puzynin. On the convergence of iterations on the basis of the continuous analogue of Newton's method, ZhVMiMF., 1992, vol. 32, no. 6, 846-856.
4. N. N. Kalitkin. Numerical methods. Moscow: Science, 1978.

### Short biography note

E.G. Nikonov

Doctor of Science (Phys & Math), professor;

Dubna State University,

Institute of the system analysis and management;

141980, Dubna, Moscow reg., Universitetskaya str., 19;

e-mail: e.nikonov@jinr.ru.

D.S. Kazakov

Student;

Dubna State University,

Institute of the system analysis and management;

141980, Dubna, Moscow reg., Universitetskaya str., 19;

e-mail: mitya_kazakov@inbox.ru

### Primary author

Dmitrii Kazakov
(Dubna State University)

### Co-author

Dr
Eduard Nikonov
(LIT JINR)