Estudo de alguns Métodos Numéricos para a solução de Equações Diferenciais Ordinárias de primeira ordem - LEMOS, Teylane França (Universidade Federal do Tocantins, 2023)
In this work we will study some methods for the solution of Ordinary Differential Equations (ODE) of the first order, in order to bring a better compression on them, also we will also study some numerical methods to determine approximate values of the solution of an ODE, knowing its initial value. Some applications will be presented, through the numerical solution of initial value problems with the first-order ODE. In this way, we will study some concepts about the first-order ODE, where we will analyze the Existence and Oneness Theorem for an initial value problem (PVI), and also some methods for the solution of the first-order ODE, such as linear, separable, homogeneous and exact. Due to the difficulty of solving some ODE, and in order to determine approximate values of the PVI solution, also we will study some single-step numerical methods, such as the Euler method, the Taylor method of higher-order, and Runge-Kutta. To exemplify some of the numerical methods that we will study, we bring some applications considering PVIs.