Welcome to our repository dedicated to the implementations of various numerical methods using the Fortran programming language. We offer a wide range of methods that can be utilized in many fields of study, from solving ordinary differential equations, numerical interpolation, to finding roots of equations, and much more.
data: This directory stores data files that serve as input for our demonstration programs.modules: This directory contains Fortran modules for distinct numerical methods.outputs: This directory is used for storing output files generated by our demonstration programs.trash: This is a temporary holding directory for ephemeral files and files that are currently in the process of organization.
Below is a list of our main programs and the numerical methods they implement. Each table entry indicates the current implementation status. We continue to work on this repository and expect to complete unfinished methods soon.
| Main Program | Method | Status |
|---|---|---|
main_derivative.f90 |
Numerical Derivatives | ✔️ |
main_integration.f90 |
Trapezoidal Method | ✔️ |
| Simpson's 1/3 Method | ✔️ | |
| Simpson's 3/8 Method | ✔️ | |
| Romberg Method | ✔️ | |
| Gaussian Quadrature | ❌ |
| Main Program | Method | Status |
|---|---|---|
main_interpolation.f90 |
Lagrange Interpolation | ✔️ |
| Newton's Forward Interpolation | ✔️ | |
| Newton's Backward Interpolation | ❌ | |
| Spline Interpolation | ❌ |
| Main Program | Method | Status |
|---|---|---|
main_ode.f90 |
Euler's Method (1st Order) | ✔️ |
| Runge-Kutta 2nd Order (1st Order) | ✔️ | |
| Runge-Kutta 4th Order (1st Order) | ✔️ | |
| Euler's Method (2nd Order) | ✔️ | |
| Verlet Method (2nd Order) | ✔️ | |
| Runge-Kutta 2nd Order (2nd Order) | ✔️ | |
| Runge-Kutta 4th Order (2nd Order) | ✔️ |
| Main Program | Method | Status |
|---|---|---|
main_random_methods.f90 |
Monte Carlo Method | ✔️ |
| Monte Carlo Integration | ✔️ | |
| Double Integral Monte Carlo | ✔️ |
| Main Program | Method | Status |
|---|---|---|
main_root_finding.f90 |
Bisection Method | ✔️ |
| Secant Method | ✔️ | |
| Newton's Method for Root Finding | ✔️ | |
| Fixed-Point Iteration | ❌ |
| Main Program | Method | Status |
|---|---|---|
main_pde.f90 |
Finite Difference Method | 🔄 |
| Finite Element Method | 🔄 | |
| Crank-Nicolson Method | 🔄 |
| Main Program | Method | Status |
|---|---|---|
main_optimization.f90 |
Gradient Descent Method | 🔄 |
| Newton's Method for Optimization | 🔄 | |
| Genetic Algorithm | 🔄 | |
| Simulated Annealing | ❌ |
| Main Program | Method | Status |
|---|---|---|
main_matrix_computations.f90 |
Matrix Inversion | 🔄 |
| Matrix Determinant | 🔄 | |
| Eigenvalues and Eigenvectors | 🔄 | |
| LU Decomposition | ❌ |
| Main Program | Method | Status |
|---|---|---|
main_statistical_methods.f90 |
Least Squares Regression | 🔄 |
| Principal Component Analysis | 🔄 | |
| Bootstrap Resampling | 🔄 | |
| Chi-Square Test | ❌ |
✔️ - Completed and available for use.
❌ - Not yet implemented.
... - Partially implemented or under development.
🔄 - To Do
This repository is under active development. If a method is not currently available or under development, please check back for updates. Contributions are always welcome.
[Additional methods and their respective example usage can be found in the full
to maintain a conversational pace.
Follow these steps to compile and run any of the main programs:
-
Navigate to the repository root directory.
-
Compile the desired main program using
gfortran. For instance, to compilemain_derivative.f90, run:
gfortran modules/edo_solution.f90 main_edo.f90 -o main_edo.out - Run the compiled program. For example, to execute
main_derivative.out, run:
./main_edo.out
We appreciate and welcome all contributions. Kindly create a branch from your fork and submit a pull request detailing your changes.
This project operates under the MIT License. Please see the LICENSE file for more comprehensive details.
Please note: It's essential to provide a copy of the license or a link to it. The readme mentions that the project is under the MIT License but does not provide a copy or a link. The missing part of the license makes it unclear what rules apply to people who want to use, change, or contribute to the software.