CS_PHY_Sem6 — Computational Physics Codes (BSMS Semester 6)

This repository contains a collection of Python scripts developed and used during my 6th semester at IISER Kolkata for solving various computational physics problems. Each module demonstrates fundamental numerical techniques essential for modeling, simulation, and data analysis in physics.

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1. Root Finding Algorithms

• Bisection Method
• Newton-Raphson Method (Tangent Method)
• Secant Method

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2. Numerical Differentiation & Integration

• Differentiation:
  • Forward Difference
  • Backward Difference
  • Central Difference
  • Five-point Approximation
• Curve Fitting:
  • Linear Least Squares Method
• Integration:
  • Trapezoidal Rule
  • Simpson’s 1/3 Rule
  • Simpson’s 3/8 Rule
  • Bode’s Rule

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3. Solving Ordinary Differential Equations (ODEs)

Numerical solvers for initial value problems (IVPs):

• Euler Method
• Midpoint Method
• Runge-Kutta 4th Order (RK4)
• Verlet Methods:
  • Standard Verlet
  • Velocity Verlet
  • Leapfrog Integration

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4. Boundary Value Problems (BVPs)

Techniques to solve second-order differential equations with boundary conditions:

• Shooting Method – implemented in solution01
• Crank–Nicolson Method with Thomas Algorithm – implemented in solution02

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5. Time-Dependent Schrödinger Equation (TDSE)

Numerical approach for solving the 1D TDSE using:

• Strang Splitting Approximation + Fast Fourier Transform (FFT) & Inverse FFT

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6. Random Number Simulations

Exploratory simulations using pseudo-randomness:

• 1D Random Walk
• Buffon’s Needle Problem
• more...

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7. Monte Carlo Techniques

Sampling-based numerical integration and probabilistic modeling:

• Monte Carlo Integration
• Importance Sampling
• Metropolis Algorithm

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Notes

• adaptive_time_stepping is not yet implemented, but the problem and reference material are included for future completion.