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Numerical Methods for Singular Boundary Value Problems
SIAM Journal on Numerical Analysis, 1975The authors treat some nonlinear two-point boundary value problems for certain ordinary differential equations having singular coefficients. Typically these problems arise when reducing partial to ordinary differential equations by physical symmetry.
Russell, R. D., Shampine, L. F.
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Singular Boundary Method for Various Exterior Wave Applications
International Journal of Computational Methods, 2015This paper presents an improved singular boundary method (ISBM) to various exterior wave applications. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions.
Fu, Zhuo-Jia +3 more
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Numerical treatment of acoustic problems with boundary singularities by the singular boundary method
Journal of Sound and Vibration, 2014Abstract The singular boundary method (SBM) is a novel boundary-type meshless method based on the fundamental solution of the given governing equation. The SBM employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions.
Lin, Ji, Chen, Wen, Chen, C. S.
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Fractal Cubic Spline Methods for Singular Boundary-Value Problems
International Journal of Applied and Computational Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. Balasubramani +2 more
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Investigation on near-boundary solutions by singular boundary method
Engineering Analysis with Boundary Elements, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gu, Yan, Chen, Wen, Zhang, Jinyang
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The European Physical Journal Plus, 2017
A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions.
Edson Pindza, Eben Maré
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A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions.
Edson Pindza, Eben Maré
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Improved singular boundary method for elasticity problems
Computers & Structures, 2014This paper presents a simple approach to evaluate origin intensity factors of the singular boundary method (SBM), a recent strong-form boundary discretization numerical technique. The SBM overcomes the perplexing 'fictitious boundary issue' associated with the method of fundamental solutions (MFS) and in it the source points and collocation points ...
Yan Gu, Wen Chen, Xiaoqiao He
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Singular boundary method for modified Helmholtz equations
Engineering Analysis with Boundary Elements, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Wen, Zhang, Jin-Yang, Fu, Zhuo-Jia
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Singular boundary method for water wave problems
Ocean Engineering, 2015This article presents the singular boundary method (SBM) for water wave-structure interaction analysis. The SBM is a novel recent boundary meshless collocation method, which uses the singular fundamental solutions of governing equation as basis function in the interpolation formulation and introduces the concept of source intensity factors to avoid the
Zatianina Razafizana, Zhuo-Jia Fu
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Meshless singular boundary methods for biharmonic problems
Engineering Analysis with Boundary Elements, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Cheng, Li, Xiaolin
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