The Lie-group shooting method for solving nonlinear singularly perturbed boundary value problems
Resource
Communications in Nonlinear Science and Numerical Simulation, 17(4), 1506-1521
Journal
Communications in Nonlinear Science and Numerical Simulation
Pages
1506-1521
Date Issued
2012
Date
2012
Author(s)
Liu, Chein-Shan
Abstract
A new computational method for solving the second-order nonlinear singularly perturbed boundary value problems (SPBVPs) is provided in this paper. In order to overcome a highly singular behavior very near to the boundary as being not easy to treat by numerical method, we adopt a coordinate transformation from an x-domain to a t-domain via a rescaling technique, which can reduce the singularity within the boundary layer. Then, we construct a Lie-group shooting method (LGSM) to search a missing initial condition through the finding of a suitable value of a parameter r∈ [0, 1]. Moreover, we can derive a closed-form formula to express the initial condition in terms of r, which can be determined properly by an accurate matching to the right-boundary condition. Numerical examples are examined, showing that the present approach is highly efficient and accurate. © 2011 Elsevier B.V.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
35.pdf
Size
23.23 KB
Format
Adobe PDF
Checksum
(MD5):ed4b6e385be725ccc38861e7b5921f9e