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Solving Differential Equations Using MATLAB/Simulink

Frank W. Pietryga, P.E.

University of Pittsburgh at Johnstown

Abstract

During the sophomore year, the mechanical and civil engineering technology students are required to complete a course in computer systems, programming and applications. The selected software package for this course was MATLAB designed and developed by the Mathworks 1. Each student was provided with a student version of the programming software. After the introductory material had been covered, the latter part of the course was used to solve basic differential equations using the MATLAB symbolic equation solver and the built-in plotting capabilities 2. Also, the students were provided instruction on Simulink. Simulink is a graphical programming language that uses MATLAB as the computational engine. Finally, methods are presented that allow the student to use both programming tools in conjunction with one another. The students were given the opportunity to contrast the techniques of solving differential equations using classical mathematical methods and the computer.

The students experienced actual hands on programming time with the instructor during the laboratory period of this course. The students seemed to really enjoy these methods and were much more comfortable with the graphical results.

Introduction

Many applications in electrical, mechanical and civil engineering technology require solving differential equations. Often, the solutions of such equations require a substantial amount of time and effort by the student. The mathematical solution of these equations does not readily provide the student with a “graphical picture” of the result. Therefore, students are uncomfortable with the entire process of solving these types of systems. Using MATLAB/Simulink to solve differential equations is very quick and easy. It may also provide the student with the symbolic solution and a visual plot of the result.

This paper will examine 3 simple applications in electrical, mechanical, and civil engineering technology requiring the solution of a differential equation. First, the author will present a method using the symbolic processing capabilities of MATLAB to quickly code a differential equation for a graphical solution. Second, the differential equations will be modeled and solved graphically using Simulink. Finally, the author will present methods which use both MATLAB and Simulink together. The MATLAB script files being used to call a Simulink model of a

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Pietryga, F. (2005, June), Solving Differential Equations Using Matlab/Simulink Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14300