Multiquadric collocation method with integralformulation for boundary layer problems

Authors:
Leevan Ling;M. R. Trümmer
Affiliations:
Department of Mathematics, Simon Fraser University 8888 University Drive, Burnaby, BC, Canada V5A 1S6;Department of Mathematics, Simon Fraser University 8888 University Drive, Burnaby, BC, Canada V5A 1S6
Venue:
Computers & Mathematics with Applications
Year:
2004

Citing 7
Cited 8

Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems

SIAM Journal on Scientific Computing
A Multiquadric Interpolation Method for Solving Initial Value Problems

Journal of Scientific Computing
An efficient numerical scheme for Burgers' equation

Applied Mathematics and Computation
Numerical solution of differential equations using multiquadric radial basis function networks

Neural Networks
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods

SIAM Journal on Scientific Computing
Overlapping domain decomposition method by radial basis functions

Applied Numerical Mathematics
Fast learning in networks of locally-tuned processing units

Neural Computation

Adaptive multiquadric collocation for boundary layer problems

Journal of Computational and Applied Mathematics
A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

Journal of Computational and Applied Mathematics
An iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities

Applied Numerical Mathematics
Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

Computers and Structures
Integrated multiquadric radial basis function approximation methods

Computers & Mathematics with Applications
Adaptive multiquadric collocation for boundary layer problems

Journal of Computational and Applied Mathematics
Numerical simulations of 2D fractional subdiffusion problems

Journal of Computational Physics
A compact five-point stencil based on integrated RBFs for 2D second-order differential problems

Journal of Computational Physics

Quantified Score

Hi-index	0.10

Visualization

Abstract

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.