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Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments. (English) Zbl 1089.65119

Summary: We present an error estimate of the derivative approximation by the local multiquadric-based differential quadrature (LMQDQ) method. The radial basis function is different from the polynomial approximation, in which Taylor series expansion is not applicable. So, the present analysis is performed through the numerical solution of Poisson equations. It is known that the approximation error of the LMQDQ method depends on three factors, i.e. local density of knots \(h\), free shape parameter \(c\) and number of supporting knots \(n_s\). By numerical experiments, their contribution to the approximation error and correlation were studied and analysed in this paper. An error estimate \(\varepsilon\sim O((h/c)^n)\) is thereafter proposed, in which \(n\) is a positive constant and determined by the number of supporting knots \(n_s\).

MSC:

65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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