The Conical Radial Basis Function for Partial Differential Equations

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or q...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2020, Vol.2020 (2020), p.1-7
Main Authors: Zhang, J., Hou, E. R., Wang, F. Z.
Format: Article
Language:English
Subjects:
Accuracy
Boundary value problems
Chebyshev approximation
Collocation
Collocation methods
Mathematics
Methods
Partial differential equations
Radial basis function
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Summary:The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.
ISSN:2314-4629
2314-4785
DOI:10.1155/2020/6664071