Fortran Numerical Methods

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.

Repository Structure

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.

Featured Programs and Method Implementations

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.

Numerical Methods Status

Differentiation and Integration

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	❌

Interpolation Methods

Main Program	Method	Status
`main_interpolation.f90`	Lagrange Interpolation	✔️
	Newton's Forward Interpolation	✔️
	Newton's Backward Interpolation	❌
	Spline Interpolation	❌

Ordinary Differential Equations

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)	✔️

Random Methods

Main Program	Method	Status
`main_random_methods.f90`	Monte Carlo Method	✔️
	Monte Carlo Integration	✔️
	Double Integral Monte Carlo	✔️

Root Finding

Main Program	Method	Status
`main_root_finding.f90`	Bisection Method	✔️
	Secant Method	✔️
	Newton's Method for Root Finding	✔️
	Fixed-Point Iteration	❌

Partial Differential Equations

Main Program	Method	Status
`main_pde.f90`	Finite Difference Method	🔄
	Finite Element Method	🔄
	Crank-Nicolson Method	🔄

Optimization

Main Program	Method	Status
`main_optimization.f90`	Gradient Descent Method	🔄
	Newton's Method for Optimization	🔄
	Genetic Algorithm	🔄
	Simulated Annealing	❌

Matrix Computations

Main Program	Method	Status
`main_matrix_computations.f90`	Matrix Inversion	🔄
	Matrix Determinant	🔄
	Eigenvalues and Eigenvectors	🔄
	LU Decomposition	❌

Statistical Methods

Main Program	Method	Status
`main_statistical_methods.f90`	Least Squares Regression	🔄
	Principal Component Analysis	🔄
	Bootstrap Resampling	🔄
	Chi-Square Test	❌

Key to Status

✔️ - 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.

Compilation and Execution Instructions

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 compile main_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

Contributing

We appreciate and welcome all contributions. Kindly create a branch from your fork and submit a pull request detailing your changes.

Licensing

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.

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