Year: 2024
Type: article
Abstract: Singularly perturbed boundary value problems (SPBVPs) plays an important role in modeling various phenomena in engineering and other science fields. The aim of this article is to compare the performance of numerical methods applied to solve the SPBVPs, which are challenging due to the presence of small perturbation parameters leading to boundary or interior layers. Four numerical methods are compared, namely, the local radial basis function method, the improved Talbot's method, the Euler's method, and the Weeks method. The main objective of this work is to improve the stability and accuracy of solutions for SPBVPs, which are important for many applications in science and engineering. We consider two-point SPBVPs with a boundary layer at one endpoint. To evaluate the performance and effectiveness of the presented numerical techniques, numerical approximations of four SPBVPs are derived and compared with the analytical solutions. The results presented in the tables and figures validate that the proposed numerical schemes are highly accurate and clearly outperform the outcomes of other methods. Furthermore, results from the functional analysis were used to study the existence of the solution to the considered model and generate sufficient requirements for Ulam-Hyers stability.
Authors: Kamran, S. Aljawi, M. Irfan, D. Santina, N. Mlaiki
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G5915967256
OpenAlex ID: W4402709044