Employ the essential and hands-on tools and functions of MATLAB's ordinary differential equation (ODE) and partial differential equation (PDE) packages, which are explained and demonstrated via interactive examples and case studies. This book contains dozens of simulations and solved problems via m-files/scripts and Simulink models which help you to learn programming and modeling of more difficult, complex problems that involve the use of ODEs and PDEs. You’ll become efficient with many of the built-in tools and functions of MATLAB/Simulink while solving more complex engineering and scientific computing problems that require and use differential equations. Practical MATLAB Modeling with Simulink explains various practical issues of programming and modelling. After reading and using this book, you'll be proficient at using MATLAB and applying the source code from the book's examples as templates for your own projects in data science or engineering. What You Will Learn Model complex problems using MATLAB and Simulink Gain the programming and modeling essentials of MATLAB using ODEs and PDEs Use numerical methods to solve 1st and 2nd order ODEs Solve stiff, higher order, coupled, and implicit ODEs Employ numerical methods to solve 1st and 2nd order linear PDEs Solve stiff, higher order, coupled, and implicit PDEs Who This Book Is For Engineers, programmers, data scientists, and students majoring in engineering, applied/industrial math, data science, and scientific computing. This book continues where Apress' Beginning MATLAB and Simulink leaves off.
Author(s): Sulaymon L. Eshkabilov
Publisher: Apress
Year: 2020
Language: English
Pages: 473
Table of Contents
About the Author
About the Technical Reviewer
Acknowledgments
Introduction
Part I: Ordinary Differential Equations
Chapter 1: Analytical Solutions for ODEs
Classifying ODEs
Example 1
Example 2
Example 3
Analytical Solutions of ODEs
dsolve()
Example 4
Example 5
Example 6
Example 7
Second-Order ODEs and a System of ODEs
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Laplace Transforms
Example 14
laplace/ilaplace
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
References
Chapter 2: Numerical Methods for First-Order ODEs
Euler Method
Example 1
Improved Euler Method
Backward Euler Method
Example 2
Midpoint Rule Method
Example 3
Ralston Method
Runge-Kutta Method
Example 4
Runge-Kutta-Gill Method
Runge-Kutta-Fehlberg Method
Adams-Bashforth Method
Example 5
Milne Method
Example 6
Taylor Series Method
Example 7
Adams-Moulton Method
Example 8
MATLAB’s Built-in ODE Solvers
Example 9
The OPTIONS, ODESET, and ODEPLOT Tools of Solvers
Example 10
Example 11
Simulink Modeling
Example 12
SIMSET
References
Chapter 3: Numerical Methods for Second-Order ODEs
Euler Method
Example 1
Example 2
Example 3
Example 4
Example 5
Runge-Kutta Method
Example 6
Example 7
Example 8
Example 9
Example 10
Adams-Moulton Method
Example 11
Example 12
Simulink Modeling
Example 13
Example 14
Example 15
Example 16
Nonzero Starting Initial Conditions
Example 17
ODEx Solvers
Example 18
Example 19
Example 20
Example 21
diff()
Example 22
Chapter 4: Stiff ODEs
Example 1
Example 2
Example 3
Example 4
Jacobian Matrix
Example 5
Example 6
Chapter 5: Higher-Order and Coupled ODEs
Fourth-Order ODE Problem
Robertson Problem
Akzo-Nobel Problem
HIRES Problem
Reference
Chapter 6: Implicit ODEs
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
References
Chapter 7: Comparative Analysis of ODE Solution Methods
Example 1
Drill Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Part II: Boundary Value Problems in Ordinary Differential Equations
Chapter 8: Boundary Value Problems
Dirichlet Boundary Condition Problem
Example 1
Example 2
Robin Boundary Condition Problem
Example 3
Sturm-Liouville Boundary Value Problem
Example 4
Stiff Boundary Value Problem
Example 5
References
Drill Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Part III: Applications of Ordinary Differential Equations
Chapter 9: Spring-Mass-Damper Systems
Single Degree of Freedom System
Case 1: Free Vibration (Motion)
Case 2: Forced Vibration (Motion)
Two Degrees of Freedom System
Three Degrees of Freedom System
Matrix Approach for n-Degree of Freedom System
References
Chapter 10: Electromechanical and Mechanical Systems
Modeling a DC Motor
Modeling a DC Motor with Flexible Load
Modeling a Microphone
Modeling Motor: Pump Gear Box
Modeling Double Pendulum
Reference
Chapter 11: Trajectory Problems
Falling Object
Thrown Ball Trajectories
References
Chapter 12: Simulation Problems
Lorenz System
Lotka-Voltera Problem
References
Drill Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Part IV: Partial Differential Equations
Chapter 13: Solving Partial Differential Equations
pdepe()
One-Dimensional Heat Transfer Problem
Example 1
Two-Dimensional Heat Transfer: Solving an Elliptic PDE with the Gauss-Seidel Method
Example 2
del2(): Laplace Operator
Example 3
Wave Equation
Solving a One-Dimensional Wave Equation
Example 4
Solving a Two-Dimensional Wave Equation
Example 5
References
Drill Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Index
