Work

Numerical algorithms using reproducing kernels for oscillatory boundary value problems

Year: 2025

Type: article

Abstract: As is known, it is perceived as a difficult problem to obtain an effective approximate solution to boundary value problems (BVPs) with highly oscillatory solutions. Traditional reproducing kernel methods (RKMs) are not effective for highly oscillatory BVPs although the RKM is a useful approach to approximation theory. The aim of the letter is to propose a novel class of RKMs to solve highly oscillatory second-order BVPs. To this end, we begin with the variation-of-constants formula (VCF). We then derive RKMs for highly oscillatory BVPs. Our simulations confirm the high accuracy of the introduced techniques.

Source: Applied Mathematics Letters

DOI: 10.1016/j.aml.2025.109794

Authors: F.Z. Geng, X.Y. Wu

Institutions: Suzhou University of Technology, Nanjing University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,800

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation