𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multiquadric collocation method with integralformulation for boundary layer problems

✍ Scribed by Leevan Ling; M.R. Trümmer

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
830 KB
Volume
48
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

Singularly perturbed boundary value problems often have solutions with very thin layers in which the solution changes rapidly. This paper concentrates on the case where theses layers occur near the boundary, although our method can be applied to problems with interior layers. One technique to deal with the increased resolution requirements in these layers is the use of domain transformations. A coordinate stretching based transform allows to move collocation points into the layer, a requirement to resolve the layer accurately. Previously, such transformations have been studied in the context of finite-difference and spectrM collocation methods. In this paper, we use radial basis functions (RBFs) to solve the boundary value problem. Specifically, we present a collocation method based on multiquadric (MQ) functions with an integral formulation combined with a coordinate transformation. We find that our scheme is ultimately more accurate than a recently proposed adaptive MQ scheme. The RBF scheme is also amenable to adaptivity.

📜 SIMILAR VOLUMES

Boundary collocation method for analyzin
Boundary collocation method for analyzing perforated plate problems
✍ C.W. Woo; L.W.Samson Chan 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 926 KB

The problem of a two-dimensional plate weakened by an array of holes of arbitrary location is analyzed using the M~khelishvili complex variable fo~~a~on and least square boundary collocation method. Several sets of complex stress functions are proposed in this article in solving the perforated plate

The collocation method based on a genera
The collocation method based on a generalized inverse multiquadric basis for bound-state problems
✍ Xu-Guang Hu; Tak-San Ho; Herschel Rabitz 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 764 KB

The generalized inverse muldquadric basis function ( ! +c21[xll 2 )-8/2, where c > 0, fl > d, and x E ]~d, is introduced for numerically solving the bound-state Schr6dinger equation. Combined with the collocation method, this basis function can yield accurate eigenvalues of highly excited vibrations

Weighted radial basis collocation method
Weighted radial basis collocation method for boundary value problems
✍ H. Y. Hu; J. S. Chen; W. Hu 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 310 KB

## Abstract This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least‐squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, how

The Galerkin-Collocation Method for Hype
The Galerkin-Collocation Method for Hyperbolic Initial Boundary Value Problems
✍ P. Dutt; A.K. Singh 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 483 KB

In this paper we implement a spectral method for solving initial boundary value problems which is in between the Galerkin and collocation methods. In this method the partial differential equation and initial and boundary conditions are collocated at an overdetermined set of points and the approximat