Abstract
We present a method of numerical integration of singularly perturbed boundary-value problems with a small parameter, based on introducing a new nonlocal independent variable. As a result, we obtain more suitable problems that allow the application of standard fixed-step numerical methods. Two test boundary-value problems for second-order ODEs that have monotonic and non-monotonic exact or asymptotic solutions, expressed in elementary functions, are considered. Comparison of numerical, exact, and asymptotic solutions showed the high efficiency of the method based on generalized nonlocal transformations for solving singular boundary-value problems with a small parameter.
| Original language | English |
|---|---|
| Article number | 012047 |
| Journal | Journal of Physics: Conference Series |
| Volume | 1205 |
| Issue number | 1 |
| DOIs | |
| State | Published - 7 May 2019 |
| Externally published | Yes |
| Event | 7th International Conference Problems of Mathematical Physics and Mathematical Modelling, MPMM 2018 - Moscow, Russian Federation Duration: 25 Jun 2018 → 27 Jun 2018 |
Bibliographical note
Publisher Copyright:© 2019 Published under licence by IOP Publishing Ltd.
Keywords
- boundary layers
- nonlinear dierential equations
- nonlocal transformations
- numerical and exact solutions
- singularly perturbed boundary-value problems
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