scholarly journals A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

2007 ◽  
Vol 201 (1) ◽  
pp. 30-47 ◽  
Author(s):  
N. Mai-Duy ◽  
R.I. Tanner
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Boundary Value ◽  
Spectral Collocation Method ◽  
Two Dimensional ◽  
Spectral Collocation

scholarly journals Rational Spectral Collocation Combined with the Singularity Separated Method for a System of Singularly Perturbed Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Lufeng Yang
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Numerical Experiments ◽  
Original Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Barycentric Form ◽  
Theoretical Results

A novel rational spectral collocation method is presented combined with the singularity-separated technique for a system of singularly perturbed boundary value problems. The solution is expressed as u=w+v, where w is the solution of the corresponding auxiliary boundary value problem and v is a singular correction with explicit expressions. The rational spectral collocation method in barycentric form with the sinh transformation is applied to solve the auxiliary third boundary problem. The parameters of the singular correction can be determined by the boundary conditions of the original problem. Numerical experiments are carried out to support theoretical results and provide a favorable comparison with research results of other work.

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