Duration: Two-Months (Four hours/ Week) Total 50+ hours

Time: 7:00 PM to 8:00PM IST

Course Fee: 599 INR (Including GST+ Gateway Charges)

For International Learner: 50 USD

Registration

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Program Overview

The certificate course “MATLAB ODE Exploration: Unveiling Numerical Methods’ Potential” provides a comprehensive introduction to the application of numerical methods for solving Ordinary Differential Equations (ODEs) using MATLAB. Participants will delve into the fundamental concepts of ODEs and explore various numerical techniques for solving them, gaining hands-on experience through practical exercises and projects. The course covers key MATLAB functions and tools specifically designed for ODE analysis, allowing participants to develop a solid understanding of how to implement and optimize numerical solutions. With a focus on both theoretical foundations and practical applications, this course equips learners with the skills to tackle real-world problems across scientific, engineering, and mathematical domains. Upon completion, participants will receive a certificate, validating their proficiency in MATLAB-based ODE exploration and numerical methods.

Why ordinary differential equations:

Ordinary Differential Equations (ODEs) find widespread applications across various scientific and engineering disciplines. In physics, ODEs are utilized to model the motion of celestial bodies, the behavior of fluid dynamics, and the dynamics of mechanical systems. In biology, ODEs describe population growth, the kinetics of chemical reactions, and the dynamics of biochemical processes. Engineers use ODEs to analyze electrical circuits, control systems, and structural dynamics. Environmental scientists employ ODEs to model the dispersion of pollutants in air and water. Additionally, ODEs play a crucial role in economics, where they model economic growth, resource allocation, and market dynamics. The versatility of ODEs makes them a powerful tool for understanding and predicting the dynamic behavior of complex systems in various fields.

Why Numerical Methods for ODE:

Numerical methods for ordinary differential equations (ODEs) are indispensable in solving complex real-world problems that lack analytical solutions. Many ODEs arising from scientific, engineering, and mathematical models cannot be solved algebraically, making numerical methods the primary approach for obtaining approximate solutions. These methods enable the efficient and accurate simulation of dynamic systems, facilitating insights into phenomena ranging from celestial motion to biochemical reactions. Numerical solutions are crucial for understanding complex behaviors and making predictions in fields such as physics, biology, engineering, and finance. Moreover, the ability to compute numerical solutions using tools like MATLAB enhances the speed and scalability of analyses, making it feasible to tackle intricate problems that would otherwise be intractable through analytical means. In essence, numerical methods for ODEs serve as a cornerstone for advancing our comprehension and manipulation of dynamic processes in diverse scientific and engineering domains.

Targeted Audience:

This program on “MATLAB ODE Exploration: Unveiling Numerical Methods’ Potential” is designed for students in UG/PG, researchers, engineers, and professionals across scientific and engineering disciplines who seek a comprehensive understanding of numerical methods for solving Ordinary Differential Equations (ODEs) using MATLAB.

Content

Introduction to MATLAB Essential

1. MATLAB Environment:

• Command Window: This is where you can directly enter commands and see the output.
• Workspace: Displays variables currently in memory.
• Editor: Used for creating, editing, and running script files.

2. Variables and Data Types:

• MATLAB supports various data types like double, single, int8, int16, int32, int64, uint8, uint16, uint32, uint64, char, and logical.
• Variables are created simply by assigning a value to a name (e.g., a = 5).

3. Basic Operations:

• Arithmetic operations: +, -, *, /, ^ (for addition, subtraction, multiplication, division, and exponentiation).
• Element-wise operations: Add a dot before operators (e.g., .* for element-wise multiplication).

4. Matrices and Arrays:

• MATLAB is particularly powerful with matrices and arrays.
• Creating matrices: A = [1, 2, 3; 4, 5, 6; 7, 8, 9].
• Accessing elements: A(2, 3) gives the element in the second row and third column.

5. Functions and Plotting:

• Basic functions: MATLAB has numerous built-in functions like sin(), cos(), exp(), etc.
• Plotting: Use commands like plot(), xlabel(), ylabel(), title(), legend() for basic plotting.

6. Control Flow:

• MATLAB supports standard control flow statements like if, else, for, and while.

7. Scripts and Functions:

• Scripts: A sequence of MATLAB commands saved in a file with a .m extension.
• Functions: Named blocks of code that can take input arguments and return outputs.

8. Getting Help:

• Use the help command to get information about functions or consult MATLAB documentation.

9. File I/O:

• Read and write data from and to files using functions like load(), save(), fprintf(), fscanf(), etc.

Numerical Methods for ODE

1. Euler’s Method:

• Brief explanation of the Euler’s Method.
• Demonstration of the algorithm.
• Practical implementation in MATLAB.
• Advantages and limitations.

2. Improved Euler Method (Heun’s Method):

• Overview of Heun’s Method.
• Comparison with Euler’s Method.
• MATLAB implementation.
• Discussion on accuracy improvements.

3. Runge-Kutta Methods (RK2, RK4):

• Introduction to Runge-Kutta Methods.
• Detailed explanation of RK2 and RK4.
• Implementation in MATLAB.
• Comparison of different orders.

4. Adams-Bashforth Methods:

• Introduction to explicit multistep methods.
• Adams-Bashforth as a predictor method.
• MATLAB demonstration.
• Application examples.

5. Adams-Moulton Methods:

• Implicit multistep methods.
• Adams-Moulton as a corrector method.
• MATLAB implementation.
• Comparison with Adams-Bashforth.

6. Backward Euler Method:

• Overview of the implicit Backward Euler Method.
• MATLAB coding.
• Discussion on stability and applications.

7. Crank-Nicolson Method:

• Explanation of the Crank-Nicolson scheme.
• MATLAB implementation.
• Comparison with other methods.

8. Predictor-Corrector Methods:

• General concept of predictor-corrector schemes.
• Examples of predictor-corrector pairs.
• MATLAB implementation.

9. Finite Difference Methods:

• Overview of finite difference schemes.
• MATLAB coding for ODEs using finite differences.

10. Finite Element Methods:

• Introduction to finite element discretization.
• MATLAB implementation.
• Application to ODEs.

11. Shooting Methods:

• Explanation of the shooting method.
• MATLAB coding for boundary value problems.

12. Boundary Value Methods:

• Overview of solving ODEs with specified boundary conditions.
• MATLAB demonstration.

13. Stiff ODE Solvers (Implicit methods):

• Discussion on stiff ODEs.
• Overview of implicit methods.
• MATLAB implementation.

14. Symplectic Integrators:

• Introduction to symplectic integrators.
• MATLAB coding for Hamiltonian systems.

15. Taylor Series Methods:

• Explanation of Taylor series methods.
• Practical implementation in MATLAB.

16. Multistep Methods:

• General concept of multistep methods.
• MATLAB coding for multistep ODE solvers.

17. Galerkin Methods:

• Introduction to Galerkin methods.
• Application to ODE problems.
• MATLAB coding.

18. Boundary Element Methods (BEM):

• Overview of boundary element discretization.
• Application to ODEs.
• MATLAB coding.

19. Spectral Methods:

• Explanation of spectral methods.
• MATLAB implementation for ODEs.

20. Chebyshev Methods:

• Overview of Chebyshev methods.
• MATLAB coding.
• Applications in ODEs.

For more information contact:

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organized by

MathTech Thinking Foundation (MTTF), India