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

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 deri...

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Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 4; pp. 7891 - 7905
Main Authors Wu, Min, Zhou, Jiali, Guan, Chaoyue, Niu, Jing
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2025
Subjects
legendre polynomials
linear operator
multiple interface problems
reproducing kernel method
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ISSN2473-6988
2473-6988
DOI10.3934/math.2025362

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025362