Document Type
Article
Source of Publication
International Journal of Mathematics and Computer in Engineering
Publication Date
2-2-2026
Abstract
This paper presents a novel numerical approach for solving the partial differential equations (PDEs), focusing on the Diffusion equation. The method combines a collocation approach with wavelet techniques to achieve high accuracy in approximating solutions. A detailed framework for the proposed method, explaining the discretization process at multiple collocation points and the formulation of the resulting system of linear equations is provided. An implementation is conducted to demonstrate the method's effectiveness in capturing the complex behaviors typical of the model studied. Comparisons with analytical solutions underscore the robustness and precision of the technique, paving the way for its application in diverse fields such as physics, finance, and engineering.
DOI Link
ISSN
Publisher
Walter de Gruyter GmbH
Disciplines
Life Sciences
Keywords
biorthogonal spline wavelets, boundary conditions, collocation methods, Diffusion equation, PDEs
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Mohammad, Mutaz and Trounev, Alexander, "A robust framework for solving PDEs: Biorthogonal spline wavelet methods" (2026). All Works. 7913.
https://zuscholars.zu.ac.ae/works/7913
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Hybrid: This publication is openly available in a subscription-based journal/series