Year: 2025
Type: article
Abstract: This research presents a comparative analysis of numerical methods for solving first-kind Fredholm integral equations using the Bubnov–Galerkin method with various wavelet and orthogonal polynomial bases. The bases considered are constructed from Legendre, Laguerre, Chebyshev, and Hermite wavelets, as well as Alpert multiwavelets and CAS wavelets. The effectiveness of these bases is evaluated by measuring errors relative to known analytical solutions at different discretization levels. Results show that global orthogonal systems—particularly the Chebyshev and Hermite—achieve the lowest error norms for smooth target functions. CAS wavelets, due to their localized and oscillatory nature, produce higher errors, though their accuracy improves with finer discretization. The analysis has been extended to incorporate perturbations in the form of additive noise, enabling a rigorous assessment of the method’s stability with respect to different wavelet bases. This approach provides insight into the robustness of the numerical scheme under data uncertainty and highlights the sensitivity of each basis to noise-induced errors.
Source: Computation
Institution: Al-Farabi Kazakh National University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,172
OpenAlex ID: W4413286449