Euler Integration

This project implements the Euler method for numerical integration of ordinary differential equations (ODEs). The Euler method is a simple and widely used numerical technique for solving initial value problems.

Features

Performs numerical integration using the Euler method.
Supports custom differential equations defined as Python functions.
Allows customization of initial conditions, step size, and number of iterations.
Provides the computed x and y values as output.

Getting Started

To use the Euler integration code in your project, follow these steps:

Clone the repository or download the source code files.
Make sure you have Python installed on your system.
Import the euler_integration function from the source code file.
Define your differential equation as a Python function that takes x and y as parameters and returns the value of dy/dx.
Set the initial conditions (x0 and y0), step size (h), and number of iterations (n) according to your problem.
Call the euler_integration function with your differential equation function and the specified parameters.
The function will return two lists: one containing the computed x values and another containing the corresponding y values.

Example

Here's an example of how to use the Euler integration code:

from euler_integration import euler_integration

def equation(x, y):
    return x ** 2

x0 = 0  # Initial value of x
y0 = 0  # Initial value of y
h = 0.1  # Step size
n = 10  # Number of iterations

x_values, y_values = euler_integration(equation, x0, y0, h, n)

for x, y in zip(x_values, y_values):
    print(f"x = {x}, y = {y}")

In this example, we define a differential equation dy/dx = x^2 and set the initial conditions, step size, and number of iterations. The euler_integration function is called with these parameters, and the computed x and y values are printed.

Contributing

Contributions to this project are welcome. If you find any issues or have suggestions for improvements, please open an issue or submit a pull request on the GitHub repository.

License

This project is licensed under the MIT License.

Acknowledgments

The Euler method is a fundamental numerical integration technique, and this implementation is based on the mathematical principles described in various numerical analysis textbooks and resources.

References

Atkinson, Kendall E. "An Introduction to Numerical Analysis." John Wiley & Sons, 2008.
Burden, Richard L., and J. Douglas Faires. "Numerical Analysis." Brooks/Cole, Cengage Learning, 2011.

vgvr0/Euler-integration-method-for-solving-differential-equations