/Runge-Kutta-method-RK4-ODE-solver

First-order ordinary differential equation (ODE) that describes exponential decay

Primary LanguagePython

Exponential Decay ODE Solver

Overview

This Python script demonstrates the numerical solution of an exponential decay ordinary differential equation (ODE) using the fourth-order Runge-Kutta method. The ODE describes the decay of a quantity over time, and the script provides a visual representation of the decay process.

Files

  • exponential_decay_solver.py: Python script containing the ODE solver function and code to visualize the solution.

Dependencies

  • numpy: Used for numerical operations.
  • matplotlib: Used for plotting the numerical solution.

Usage

  1. Ensure you have the required dependencies installed:

    pip install numpy matplotlib

  2. Run the script:

    python rk4.py

  3. Adjust the parameters in the script, such as the initial conditions, decay rate (k), and time interval, to explore different scenarios of exponential decay.

Example

The default example in the script considers an exponential decay ODE with an initial quantity of 1, a decay rate (k) of 0.5, and a time interval from 0 to 5 with a step size of 0.1. The resulting numerical solution is plotted using Matplotlib.