Work

A numerical method using Legendre polynomials for solving two-point interface problems

Year: 2025

Type: article

Abstract: This paper presents a novel numerical algorithm that integrates reproducing kernel functions with Legendre polynomials to effectively address multiple interface problems. We create a new set of bases within the reproducing kernel space, introduce a linear operator, and utilize its properties to derive an equivalent operator equation. The model equation is then transformed into a matrix equation, enhancing the solution process for complex interface issues. Comparative numerical examples demonstrate the superior accuracy of our method over conventional approaches. Furthermore, the solution's existence and uniqueness are validated, ensuring the algorithm's reliability and effectiveness.

Source: AIMS Mathematics

DOI: 10.3934/math.2025362

Authors: Min Wu, Jiali Zhou, Chaoyue Guan, Jing Niu

Institutions: Zhejiang University of Science and Technology, Zhejiang University of Technology, Harbin Normal University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4409117621