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Wavelet Multi-Resolution Interpolation Galerkin Method for Linear singularly perturbed boundary value problems

Computer Modeling in Engineering & Sciences 2024年第4期139卷 297-318页

作者： Jiaqun Wang Guanxu Pan Youhe Zhou Xiaojing Liu School of Management Science and Engineering Anhui University of Finance and EconomicsBengbu233030China Key Laboratory of Mechanics on Disaster and Environment in Western China The Ministry of EducationCollege of Civil Engineering and MechanicsLanzhou UniversityLanzhou730000China

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value *** conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin *** a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep *** the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element *** numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet *** results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary *** with many other methods,the proposed method possesses satisfactory accuracy and *** 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

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B-Spline Collocation Method for Solving singularly perturbed boundary value problems

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Journal of Applied Mathematics and Physics 2016年第9期4卷 1699-1704页

作者： Bin Lin School of Mathematics and Computation Science Lingnan Normal University Zhanjiang China

We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions.

关键词： Fifth Order B-Spline Functions B-Spline Collocation Method singularly perturbed boundary value problems

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VARIABLE MESH FINITE DIFFERENCE METHOD FOR SELF-ADJOINT singularly perturbed TWO-POINT boundary value problems

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Journal of Computational Mathematics 2010年第5期28卷 711-724页

作者： Mohan K.Kadalbajoo Devendra Kumar Department of Mathematics & Statistics

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

关键词： singularly perturbed boundary value problems Finite difference method,boundary layer Parameter uniform-convergence Variable mesh.

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