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

Min Wu; Jiali Zhou; Chaoyue Guan; Jing Niu; Min Wu; Jiali Zhou; Chaoyue Guan; Jing Niu

doi:10.3934/math.2025362

AIMS Mathematics

2025, Volume 10, Issue 4: 7891-7905. doi: 10.3934/math.2025362

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

1.
School of Science, Zhejiang University of Science and Technology, 310023 Hangzhou Zhejianag, China
2.
School of Mathematical Sciences, Zhejiang University of Technology, 310023 Hangzhou Zhejianag, China
3.
School of Mathematical Science, Harbin Normal University, 150025 Harbin Heilongjiang, China

Received: 06 December 2024 Revised: 19 March 2025 Accepted: 26 March 2025 Published: 03 April 2025
MSC : 41A10, 46E22

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.
- Legendre polynomials,
- multiple interface problems,
- reproducing kernel method,
- linear operator
Citation: Min Wu, Jiali Zhou, Chaoyue Guan, Jing Niu. A numerical method using Legendre polynomials for solving two-point interface problems[J]. AIMS Mathematics, 2025, 10(4): 7891-7905. doi: 10.3934/math.2025362

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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.

References

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