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

In this article, we present an error estimate of the derivative approximation by the local multiquadricbased differential quadrature (LMQDQ) method. 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 equation. It is known that the approximation error of LMQDQ method depends on three factors, i.e. local density of knots h, free shape parameter c and number of supporting knots ns. By numerical experiments, their contribution to the approximation error and correlation were studied and analysed in this paper. An error estimate ∼ O((h/c)n) is thereafter proposed, in which n is a positive constant and determined by the number of supporting knots ns.