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The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems

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  • Karageorghis, Andreas
  • Tappoura, Demetriana
  • Chen, C.S.

Abstract

We consider the application of the Kansa-radial basis function (RBF) collocation method to two-dimensional fourth order boundary value problems (BVPs). The presence of two boundary conditions makes it necessary to use a second set of centres corresponding to the second boundary condition. One option is to take these centres on the boundary but at different positions to the original boundary centres. A second option is to place them on a curve surrounding the physical boundary of the problem under consideration. The two approaches are applied to several numerical examples and their results are compared and analysed.

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  • Karageorghis, Andreas & Tappoura, Demetriana & Chen, C.S., 2021. "The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 581-597.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:581-597
    DOI: 10.1016/j.matcom.2020.10.010
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    Cited by:

    1. Karageorghis, Andreas, 2022. "A time–efficient variable shape parameter Kansa–radial basis function method for the solution of nonlinear boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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