Mathematical Modeling of Differential Equations as Applied to Problems of Physics and Electrical Engineering

Abstract

Mathematical modeling of differential equations as applied to problems of physics and electrical engineering in the MatLab/Simulink environment is considered. The MatLab software package is designed to provide analytical and numerical solutions for various mathematical problems and simulate complex technical objects and systems. The Simulink app is one of the tools within the MatLab package. It has major structured, object-oriented, and visual programming capabilities. We reviewed both the simplest equations (a first-order differential equation) and more complex linear and nonlinear differential equations of the first and second orders. For the first-order linear differential equation, we have a complete correlation of modeling results. When solving the second-order non-linear differential equation, we observed small result deviations due to the method selected and the integration step. We used the example of the practical application of the MatLab/Simulink environment to calculate the parameters of an electric circuit. Found the relationship between the current and the modeling time in the series-oscillatory circuit with a harmonic alternating voltage source. It is reduced to solving a nonhomogeneous linear differential equation with constant second-order coefficients describing the forced current change in the oscillatory circuit following the second Kirchhoffs law.