Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions

Chein-Shan Liu; Botong Li

Applications of Mathematics (2019)

  • Volume: 64, Issue: 6, page 679-693
  • ISSN: 0862-7940

Abstract

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For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly find accurate numerical solutions for the highly singularly perturbed problems by a simple collocation technique.

How to cite

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Liu, Chein-Shan, and Li, Botong. "Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions." Applications of Mathematics 64.6 (2019): 679-693. <http://eudml.org/doc/294348>.

@article{Liu2019,
abstract = {For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly find accurate numerical solutions for the highly singularly perturbed problems by a simple collocation technique.},
author = {Liu, Chein-Shan, Li, Botong},
journal = {Applications of Mathematics},
keywords = {singularly perturbed ODE; Robin boundary function; energetic Robin boundary function; collocation method},
language = {eng},
number = {6},
pages = {679-693},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions},
url = {http://eudml.org/doc/294348},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Liu, Chein-Shan
AU - Li, Botong
TI - Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 6
SP - 679
EP - 693
AB - For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly find accurate numerical solutions for the highly singularly perturbed problems by a simple collocation technique.
LA - eng
KW - singularly perturbed ODE; Robin boundary function; energetic Robin boundary function; collocation method
UR - http://eudml.org/doc/294348
ER -

References

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