| Title |
M-matrices, chebyshev polynomials and applications for finite difference schemes / |
| Translation of Title |
M-matricos, Čebyševo polinomai ir taikymas baigtinių skirtumų schemoms. |
| Authors |
Yousaf, Umair |
| Full Text |
|
| Pages |
44 |
| Keywords [eng] |
M-matrices, Chebyshev polynomials, Elliptic Equations, Kronecker Product, Poisson Equation |
| Abstract [eng] |
This study develops a framework that combines $M$-matrix theory and Chebyshev polynomials to improve the stability and accuracy of finite difference methods. We use key $M$-matrix traits invertibility, non-positive off-diagonals, and diagonal dominance to ensure stable discretizations that converge reliably. Chebyshev polynomials help improve spectral approximations, reduce oscillations, and speed up solvers. This combined approach tackles stability issues in problems with steep gradients or ill-conditioned systems. Analysis and experiments show it delivers better error bounds, less sensitivity to grid choice, and higher efficiency. Tests on boundary layers and high-dimensional PDEs confirm the framework's practical value for robustly simulating complex phenomena, demonstrating how merging matrix algebra and polynomial techniques advances numerical methods. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Master thesis |
| Language |
English |
| Publication date |
2025 |
