### Abstract

Original language | English |
---|---|

Pages (from-to) | 381-405 |

Number of pages | 24 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 131 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- uniform convergence
- adaptivity
- equidistribution
- singular perturbation
- reaction-diffusion
- computational mathematics

### Cite this

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*Journal of Computational and Applied Mathematics*, vol. 131, no. 1-2, pp. 381-405. https://doi.org/10.1016/S0377-0427(00)00260-0

**On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution.** / Beckett, G.; Mackenzie, J.A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution

AU - Beckett, G.

AU - Mackenzie, J.A.

PY - 2001

Y1 - 2001

N2 - We examine the convergence properties of a finite difference approximation of a singularly perturbed reaction-diffusion boundary value problem using a nonuniform grid. The grid is based on the equidistribution of a positive monitor function that is a linear combination of a constant floor and a power of the second derivative of the solution. Analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter. The use of equidistribution principles appears in many practical grid adaption schemes and our analysis provides insight into the convergence behaviour on such grids. Numerical results are given that confirm the uniform convergence rates.

AB - We examine the convergence properties of a finite difference approximation of a singularly perturbed reaction-diffusion boundary value problem using a nonuniform grid. The grid is based on the equidistribution of a positive monitor function that is a linear combination of a constant floor and a power of the second derivative of the solution. Analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter. The use of equidistribution principles appears in many practical grid adaption schemes and our analysis provides insight into the convergence behaviour on such grids. Numerical results are given that confirm the uniform convergence rates.

KW - uniform convergence

KW - adaptivity

KW - equidistribution

KW - singular perturbation

KW - reaction-diffusion

KW - computational mathematics

UR - http://dx.doi.org/10.1016/S0377-0427(00)00260-0

U2 - 10.1016/S0377-0427(00)00260-0

DO - 10.1016/S0377-0427(00)00260-0

M3 - Article

VL - 131

SP - 381

EP - 405

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -