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

作　　者：Jiaqun Wang Guanxu Pan Youhe Zhou Xiaojing Liu 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2024年第4期297-318,共22页工程与科学中的计算机建模（英文）

基　　金：supported by the National Natural Science Foundation of China (No.12172154);the 111 Project (No.B14044);the Natural Science Foundation of Gansu Province (No.23JRRA1035);the Natural Science Foundation of Anhui University of Finance and Economics (No.ACKYC20043).

摘　　要：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 proposedwavelet method.The results showthat the use ofmodified 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 theε-uniform convergence of this wavelet method can reach 5.

关 键 词：Wavelet multi-resolution interpolation Galerkin singularly perturbed boundary value problems mesh-free method Shishkin node boundary layer 

分 类 号：O17[理学—数学]