Ordinary Differential Equations (ODEs) using various methods such as Euler’s and Runga-Kutta methods.

Aim

The aim of this experiment is to solve Ordinary Differential Equations (ODEs) numerically using a simulation tool by performing the following steps:

  1. To input a first-order differential equation in the form dy/dt, where 'y' is the dependent variable and 't' is the independent variable.
  2. To define the initial condition of the system by specifying the initial time and initial value of the function.
  3. To select numerical solution techniques such as:
    • Euler’s Method
    • 4th Order Runge-Kutta Method
  4. To compute the approximate solution of the ODE over a given time interval by dividing it into a specified number of steps.
  5. To visualize the numerical solution graphically to observe the behavior of the system over time.
  6. To compare the accuracy and stability of different numerical methods for solving ODEs.
  7. To understand the practical importance of numerical ODE solvers when analytical solutions are difficult or impossible to obtain.