This repository contains the complete set of numerical experiments conducted as part of my Master’s Thesis project, titled "Theoretical and Computational Considerations of Sturm-Liouville Systems."
The codes explore various aspects of spectral methods, Fourier analysis, and Chebyshev polynomial-based approximations, among other related techniques in computational differential equations.
Below is a brief overview of the main code files included:
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CODE CHUNK – FOURIER ANALYSIS.ipynb
Jupyter Notebook containing experiments related to Fourier-based approximations used in the analysis. -
CODE FOR FIGURE 12.nb
Mathematica notebook with computational visualizations for Figure 12. -
CODE FOR FIGURE 14 AND 15.nb
Mathematica notebook corresponding to Figures 14 and 15.
All code files are well-commented and designed to be self-explanatory, enabling easy navigation and replication of the experiments.
- Python – For implementing core numerical methods and visualizations.
- Mathematica – For symbolic computation and high-precision visual analysis.
- MATLAB – Used in parts of the thesis for matrix-based implementations (not shown in the current list but mentioned for completeness).
The numerical experiments in this repository were developed to support theoretical investigations in:
- Sturm-Liouville boundary value problems
- Spectral and pseudo-spectral approximation techniques
- Numerical treatment of eigenvalue problems
- Role of orthogonal polynomials (e.g., Chebyshev) in approximation theory
These codes were developed under the supervision of Dr. Anandateertha Mangasuli & Dr. Ambuj Pandey and form a core part of the analysis documented in my MS thesis submitted at IISER Bhopal.
This project is shared for academic and educational purposes. Please cite appropriately if you reuse or build upon this work.