https://doi.org/10.36719/2663-4619/109/142-149
Saltanat Veysova
Military Institute named after H. Aliyev
Candidate of Physical and Mathematical Sciences
seltenet.veysova63@gmail.com
Assessment of Errors in Solving Ordinary Differential
Equations Using the Picard Method
Abstract
The article shows the theoretical foundations of the method for constructing solutions to ordinary differential equations using the Picard method, provides a different formulation of the mentioned theorems and statements, and also reflects the corresponding proof mechanism. In the solving differential equations, the uniform convergence of successive approximations to any function from a given set is investigated and it is shown that the limit in this approximation is a solution to the integral equation. In the process of research, it was also explained that all uniform convergence of successive approximations are located inside a certain rectangle, and it was also shown that, according to classical theory, the solution of the equation does not extend beyond only a limited area.
Keywords: picard approach, existence and uniqueness of the solution, Lipschitz condition, integral equation, successive approximation, uniform convergence