Practical MATLAB Modeling with Simulink : Programming and Simulating Ordinary and Partial Differential Equations

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. 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 Employ the essential and hands-on tools and functions of the MATLAB's ordinary differential equations (ODEs) and partial differential equations (PDEs) 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. Youll 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 How to model more complex problems using MATLAB and Simulink Gain the programming and modeling essentials of MATLAB using ODEs and PDEs How to program and use numerical methods to solve 1st and 2nd order ODEs How to program and solve stiff, higher order, coupled and implicit ODEs How to program and use numerical methods to solve 1st and 2nd order linear PDEs How to program and solve stiff, higher order, coupled and implicit PDEs 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. 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****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.