An Initial-Value Algorithm for solving a Class of Non-Linear Singularly Perturbed Two-point Boundary Value Problems | ||||
| The International Conference on Mathematics and Engineering Physics | ||||
| Article 8, Volume 5, International Conference on Mathematics and Engineering Physics (ICMEP-5), May 2010, Page 1-10 PDF (250.33 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/icmep.2010.29776 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| E. R. El-Zahar | ||||
| Abstract | ||||
| Abstract We consider non-linear singular perturbation problems of the form y (x ) p(y (x ))y (x ) q(x , y (x )) r (x ) , y (0) , y (1) with a boundary layer at one end point. The method is distinguished by the following fact: The original problem is reduced to an asymptotically equivalent first order initial value problem (IVP). Then, an initial-value algorithm is applied to solve this IVP. The algorithm is based on the locally exact integration of a linearized problem on a non-uniform mesh. Two terms recurrence relation with controlled step size is obtained. Several problems are solved to demonstrate the applicability and efficiency of the algorithm. It is observed that the present method approximates the exact solution very well. | ||||
| Keywords | ||||
| Two-point boundary value problems; Singular perturbation problems; Boundary layer; Initial-value problems; Nonuniform mesh | ||||
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