Mathematical modeling in informatiсs lessons using numerical solution of differential equations

Abstract

The article considers the author's fragment of an in-depth course of informatics in a physics and mathematics school. It is based on the use of differential equations to model complex physical processes. Three models are considered: a mathematical spring pendulum, the orbital motion of the satellite around the planet and the movement of the body in the atmosphere taking into account air resistance. Since in the in-depth course of mathematics of the physics and mathematics school, numerical methods for solving differential equations are not studied, the article proposes to use the simplest method — the Euler method. Using this method, the resulting differential equations in each case are numerically solved. Since differential equations arising in each model have a second order, in order to apply the Euler method, it is necessary to reduce the order of differential equations by introducing new variables. In this case, instead of one differential equation of the second order, a system of two equations of the first order arises. For each built model, its implementation in the PascalABC.NET programming language is given.