https://github.com/aantusahaa/fortran-lab
This repository contains a collection of numerical methods implemented in modern Fortran. These methods are widely used in scientific computing, engineering simulations, and mathematical problem-solving.
https://github.com/aantusahaa/fortran-lab
fortran numerical-analysis numerical-methods
Last synced: about 1 month ago
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This repository contains a collection of numerical methods implemented in modern Fortran. These methods are widely used in scientific computing, engineering simulations, and mathematical problem-solving.
- Host: GitHub
- URL: https://github.com/aantusahaa/fortran-lab
- Owner: aantusahaa
- Created: 2024-11-07T13:02:36.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2025-03-27T15:13:31.000Z (about 1 month ago)
- Last Synced: 2025-03-27T16:26:31.777Z (about 1 month ago)
- Topics: fortran, numerical-analysis, numerical-methods
- Language: Fortran
- Homepage:
- Size: 41 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Fortran Programming Lab II (MTHL-3206)
## Introduction
This repository contains a collection of numerical methods implemented in modern Fortran, which were learned during the course Fortran Programming Lab II (MTHL-3206). These methods are widely used in scientific computing, engineering simulations, and mathematical problem-solving. Each method is implemented in Fortran 90/95/2003/2008 style (modern Fortran).
## Index
### 1. Solution of Algebraic Equations in Single Variables
- [Bisection Method](./01-bisection-method/main.f90)
- [Method of False Position](./02-false-position/main.f90)
- [Fixed-Point Iteration Method](./03-fixed-point-iteration/main.f90)
- [Newton-Raphson Method](./04-newton-raphson/main.f90)
### 2. Interpolation and Polynomial Approximation
- [Taylor's Polynomial Approximation](./05-taylor-polynomial/main.f90)
- [Newton's Forward Difference Interpolation](./06-newton-forward-difference/main.f90)
- [Newton's Backward Difference Interpolation](./07-newton-backward-difference/main.f90)
- [Newton's Divided Difference Interpolation](./08-newton-divided-difference/main.f90)
- [Lagrange's Interpolation](./09-lagrange-interpolation/main.f90)
- [Stirling's Central Difference Interpolation](./10-stirling-central-difference/main.f90)
- [Bessel's Central Difference Interpolation](./11-bessel-central-difference/main.f90)
### 3. Differentiation and Integration
- [Forward Difference](./12-forward-difference/main.f90)
- [Backward Difference](./13-backward-difference/main.f90)
- [Central Divided Difference](./14-central-divided-difference/main.f90)
- [Richardson Extrapolation](./15-richardson-extrapolation/main.f90)
- [Trapezoidal Rule](./16-trapezoidal-rule/main.f90)
- [Simpson's 1/3 Rule](./17-simpson-1-3-rule/main.f90)
- [Simpson's 3/8 Rule](./18-simpson-3-8-rule/main.f90)
- [Weddle's Rule](./19-weddle-rule/main.f90)
### 4. Solution of Linear Systems
- [Gaussian Elimination with Backward Substitution](./20-gaussian-elimination-with-backward-substitution/main.f90)
- [Gaussian Elimination with LU Factorization](./21-gaussian-elimination-with-lu-factorization/main.f90)
- [Jacobi Method](./22-jacobi/main.f90)
- [Gauss-Seidel Method](./23-gauss-seidel/main.f90)
- [Successive Over-Relaxation(SOR) Method](./24-sor/main.f90)
### 6. Initial Value Problem for ODE
- [Picard's Method](./28-picard-method/main.f90)
- [Euler's Method](./29-euler-method/main.f90)
- [Taylor's Method](./30-taylor-method/main.f90)
- [2nd Order Runge-Kutta Method](./31-runge-kutta-order-2/main.f90)
- [4th Order Runge-Kutta Method](./32-runge-kutta-order-4/main.f90)
- [Adams-Bashforth Method](./33-adams-bashforth-method/main.f90)
- [Extrapolation Method](./34-extrapolation-method/main.f90)
- [Adaptive Euler Method](./35-adaptive-euler-method/main.f90)
- [Adaptive Runge Kutta Method](./36-adaptive-runge-kutta-method/main.f90)
## Reference used for algorithm
- Numerical Analysis (9th edition) by Richard L. Burden and J. Douglas Faires
- [Engineering Mathematics (Stirling's Central Difference Interpolation)](https://theengineeringmaths.com/wp-content/uploads/2017/11/interpolation-web.pdf)
- [LibreTexts Physics (Bessel's Central Difference Interpolation)]()
- [LibreTexts Mathematics (Richardson Extrapolation)]()
- [Adaptive Runge Kutta Method](https://jonshiach.github.io/ODEs-book/_pages/2.5_Adaptive_step_size_control.html)