Radial point interpolation collocation method (RPICM) for partial differential equations

Using a local radial basis function collocation method to approximate radiation boundary conditions

“…Although this method is simple, it usually suffers from severe illconditioning when a high resolution is required. In order to circumvent the ill-conditioning problem, a localization procedure (Lee et al, 2003;Liu et al, 2005a;Šarler and Vertnik, 2006) is introduced in the following. First, Eq.…”

“…In addition, there are also researches using the particular solutions of multiquadrics to improve the accuracy (Tsai, 2013(Tsai, , 2015Yao et al, 2011). Alternatively, Liu et al (2005aLiu et al ( , 2005b replaced the multiquadrics by the thin plate spline (Duchon, 1977) and proposed a radial point interpolation collocation method. The main concept of LRBFCM is the interpolation function values only associated with the neighboring nodes in the entire domain.…”

Modelling of Displacement Washing of Pulp Fibers Using the Hermite Collocation Method

“…To overcome this problem, the Hermite collocation method (HCM) was proposed, which is the combination of Hermite interpolating polynomials and the orthogonal collocation technique. In the Hermite collocation method cubic Hermite interpolating polynomials are used as base functions to approximate the trial function (Dyksen & Lynch, 2000;Lang & Sloan, 2002;Jung, 2003;Liu et al, 2005;Ma et al, 2006;Finden, 2007;Mazroui et al, 2007;Han, 2009;Ricciardi & Brill, 2009;Gülsu et al, 2011;Yalçinbaş et al, 2011;Orsini et al, 2011). To apply the collocation technique, the residual is set equal to zero at the collocation points.…”

Image Resolution Enhancement Method Based on Feature Space

“…The modern interpolation method is also called nonlinear interpolation, and it introduces the fractal topology, wavelet analysis, partial differential equations, nonlinear optimization theory etc. into digital image processing [7][8][9][10]. The modern interpolation methods can use different interpolation method in different regions of image according to the regulation of the image spectrum weighted coefficient.…”