Solving Differential Equations by Means of Mathematical Simulation in Simulink App of Matlab Software Package

Abstract

This work considers the use of the simulation to solve differential equations in MatLab/Simulink and its results. 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. The system can solve linear algebra problems, integral and differential equations, and perform Laplace and Fourier transformations. We reviewed both the simplest equations (a first-order differential equation) and more complex linear and non-linear differential equations of the first and second orders. The results of structured modeling (S-model) in Simulink were compared to program code results (M-file) in MatLab. 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. When discussing the results, we used the example of the practical application of the MatLab/Simulink environment to calculate the parameters of an electric circuit, namely to obtain 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 Kirchhoff’s law. In the conclusion, we note the versatility of the MatLab/Simulink modeling environment for the solution of differential equations including those with quotient derivatives.