Geodesic
Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions
Applications of Mathematics, Tome 64 (2019) no. 6, pp. 679-693 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2019.0066-19
Classification : 34B60
Keywords: singularly perturbed ODE; Robin boundary function; energetic Robin boundary function; collocation method 
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     title = {Solving second-order singularly perturbed {ODE} by the collocation method based on energetic {Robin} boundary functions},
     journal = {Applications of Mathematics},
     pages = {679--693},
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Liu, Chein-Shan; Li, Botong. Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions. Applications of Mathematics, Tome 64 (2019) no. 6, pp. 679-693. doi: 10.21136/AM.2019.0066-19

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