Mathematica-source-codes-for-various-Numerical-Analysis-papers

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Mathematica-source-codes-for-various-Numerical-Analysis-papers

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Mathematica source codes of experimental results of various papers

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# Mathematica Source Codes for Various Numerical Analysis Papers

This repository provides Mathematica source codes used to generate experimental results for several numerical analysis papers. Each directory corresponds to a specific paper and includes the relevant code and, where applicable, data files.

## Contents

- **A Novel Numerical Method of Two-Dimensional Fredholm Integral Equations of the Second Kind**
- **A New Degenerate Kernel Method for a Weakly Singular Integral Equation**
- **Fourth-Order Compact Scheme for the One-Dimensional Sine-Gordon Equation**
- **Haar Wavelet Method for Some Nonlinear Volterra Integral Equations of the First Kind**
- **Improving Petrov–Galerkin Elements via Chebyshev Polynomials and Solving Fredholm Integral Equation of the Second Kind by Them**
- **Legendre Wavelets Method for the Numerical Solution of Fractional Integro-Differential Equations with Weakly Singular Kernel**
- **Legendre Wavelets Operational Method for the Numerical Solutions of Nonlinear Volterra Integro-Differential Equations System**
- **Pouzet–Runge–Kutta–Chebyshev Method for Volterra Integral Equations of the Second Kind**
- **Wavelets Method for Solving Systems of Nonlinear Singular Fractional Volterra Integro-Differential Equations**
- **Runge–Kutta–Fehlberg Method**

## Usage

Each directory contains a Mathematica notebook (`.nb`) file. To run the code:

1. Open the `.nb` file in Mathematica.
2. Evaluate the cells sequentially to reproduce the results presented in the corresponding paper.

## References

For detailed explanations of the methods and results, please refer to the original papers associated with each directory.

## License

This repository is licensed under the [MIT License](LICENSE).

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