Open Access

ARTICLE

# Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

Jiaqun Wang1,2, Guanxu Pan2, Youhe Zhou2, Xiaojing Liu2,*

1 School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030, China
2 Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, China

* Corresponding Author: Xiaojing Liu. Email:

Computer Modeling in Engineering & Sciences 2024, 139(1), 297-318. https://doi.org/10.32604/cmes.2023.030622

## Abstract

In this study, a wavelet multi-resolution interpolation Galerkin method (WMIGM) is proposed to solve linear singularly perturbed boundary value problems. Unlike conventional wavelet schemes, the proposed algorithm can be readily extended to special node generation techniques, such as the Shishkin node. Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients. All the shape functions possess the Kronecker delta property, making the imposition of boundary conditions as easy as that in the finite element method. Four numerical examples are studied to demonstrate the validity and accuracy of the proposed wavelet method. The results show that the use of modified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer. Compared with many other methods, the proposed method possesses satisfactory accuracy and efficiency. The theoretical and numerical results demonstrate that the order of the -uniform convergence of this wavelet method can reach 5.

## Keywords

APA Style
Wang, J., Pan, G., Zhou, Y., Liu, X. (2024). Wavelet multi-resolution interpolation galerkin method for linear singularly perturbed boundary value problems. Computer Modeling in Engineering & Sciences, 139(1), 297-318. https://doi.org/10.32604/cmes.2023.030622
Vancouver Style
Wang J, Pan G, Zhou Y, Liu X. Wavelet multi-resolution interpolation galerkin method for linear singularly perturbed boundary value problems. Comput Model Eng Sci. 2024;139(1):297-318 https://doi.org/10.32604/cmes.2023.030622
IEEE Style
J. Wang, G. Pan, Y. Zhou, and X. Liu "Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems," Comput. Model. Eng. Sci., vol. 139, no. 1, pp. 297-318. 2024. https://doi.org/10.32604/cmes.2023.030622

View

Like

## Related articles

• Muhammad Shoaib Arif , Yasir Nawaz,...
• G Devaraj, Shashi Narayan, Debasish...
• Weiwei Li, Wen Chen
• Seyed Mahmoud Hosseini
• M.R. Myers, A.B. Jorge, D.E. Yuhas,...