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    Indirect RBFN Method with Thin Plate Splines for Numerical Solution of Differential Equations

    N. Mai-Duy, T. Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 85-102, 2003, DOI:10.3970/cmes.2003.004.085

    Abstract This paper reports a mesh-free Indirect Radial Basis Function Network method (IRBFN) using Thin Plate Splines (TPSs) for numerical solution of Differential Equations (DEs) in rectangular and curvilinear coordinates. The adjustable parameters required by the method are the number of centres, their positions and possibly the order of the TPS. The first and second order TPSs which are widely applied in numerical schemes for numerical solution of DEs are employed in this study. The advantage of the TPS over the multiquadric basis function is that the former, with a given order, does not contain the adjustable shape parameter (i.e. the… More >

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