| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 767106 | Communications in Nonlinear Science and Numerical Simulation | 2012 | 16 Pages |
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.
► Singularly perturbed boundary value problems were treated by a Lie-group shooting method. ► Singularity appears by using a rescaling technique. ► The missing initial condition could be expressed in term of a parameter. ► The Lie-group shooting method is effective and accurate.
