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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

 


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