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