### Abstract

Language | English |
---|---|

Pages | 269-276 |

Number of pages | 8 |

Journal | Neural, Parallel and Scientific Computations |

Volume | 24 |

Publication status | Published - 31 Aug 2016 |

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### Keywords

- finite difference
- numerical methods for ODE's
- multistep methods

### Cite this

*Neural, Parallel and Scientific Computations*,

*24*, 269-276.

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*Neural, Parallel and Scientific Computations*, vol. 24, pp. 269-276.

**On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative.** / McKee, S.; Cuminato, José A.; Mohanty, R. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative

AU - McKee, S.

AU - Cuminato, José A.

AU - Mohanty, R. K.

PY - 2016/8/31

Y1 - 2016/8/31

N2 - This note is concerned with the convergence of a finite difference scheme to the solution of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first derivative. By defining stability as the linear growth of the elements of the inverse of a certain matrix and combining this with consistency, convergence is demonstrated. This stability concept is then interpreted in terms of a root condition.

AB - This note is concerned with the convergence of a finite difference scheme to the solution of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first derivative. By defining stability as the linear growth of the elements of the inverse of a certain matrix and combining this with consistency, convergence is demonstrated. This stability concept is then interpreted in terms of a root condition.

KW - finite difference

KW - numerical methods for ODE's

KW - multistep methods

UR - http://www.dynamicpublishers.com/Neural/neuralv24.htm

UR - http://www.dynamicpublishers.org/journals/index.php/NPSC/index

M3 - Article

VL - 24

SP - 269

EP - 276

JO - Neural, Parallel and Scientific Computations

T2 - Neural, Parallel and Scientific Computations

JF - Neural, Parallel and Scientific Computations

SN - 1061-5369

ER -