Fortran Euler Method Simulation

This project implements Euler's Method in Fortran to solve the motion of a charged particle under combined electric and gravitational fields.

Problem Statement

A particle with the following properties:

• Mass: 10 gm (0.01 kg)
• Charge: 0.2 C
• Electric Field: E = 20 V/m
• Gravitational Field: g = −9.8 m/s²
• Initial Velocity: v₀ = −1.52 m/s
• Initial Position: x₀ = 7.52 m

Objective: Using Euler's Method, find the position and velocity over a suitable time interval until the velocity reaches 1.52 m/s. Calculate the percent error and generate position–time and velocity–time graphs.

Requirements

• Fortran Compiler: gfortran or equivalent
• Build System: Optional (can compile directly with gfortran)
• Plotting Tools: Python with matplotlib (optional, for visualization)

Installation & Compilation

1. Clone or download the repository:

   git clone https://github.com/Moniruz200/Fortran-Program-For-Euler-Method.git
   cd Fortran-Program-For-Euler-Method

2. Compile the Fortran source:

   gfortran -o euler_method euler_method.f90

3. Run the program:

   ./euler_method

Usage

The program executes with predefined parameters based on the problem statement. You may modify the following parameters in the source code before compilation:

• Initial velocity
• Initial position
• Time step size (dt)
• Maximum time interval

The output includes:

• Position and velocity at each time step
• Percent error calculations
• Data points for graphing (if output file is generated)

Output

The program generates:

• Console Output: Position, velocity, and error metrics at each iteration
• Output File: CSV formatted data file with results for external plotting

Author

Moniruz Zaman

License

This project is provided as-is for educational purposes.