Department of Mathematics
Multiquadric collocation method with integral formulation for boundary layer problems
Singularly perturbed boundary value problems often have solutions with very thinlayers 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 spectral 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. © 2004 Elsevier Ltd. All rights reserved.
Boundary layer, Boundary layer problems, High-order discretizations, Integral formulation, Multiquadric, Spectral accuracy
Source Publication Title
Computers and Mathematics with Applications
Ling, Leevan, and M. R. Trummer. "Multiquadric collocation method with integral formulation for boundary layer problems." Computers and Mathematics with Applications 48.6-5 (2004): 927-941.