### Abstract

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.

Original language | English |
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Pages (from-to) | 269-276 |

Number of pages | 8 |

Journal | Neural, Parallel and Scientific Computations |

Volume | 24 |

Publication status | Published - 31 Aug 2016 |

### Keywords

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

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## Cite this

McKee, S., Cuminato, J. A., & Mohanty, R. K. (2016). On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative.

*Neural, Parallel and Scientific Computations*,*24*, 269-276. http://www.dynamicpublishers.com/Neural/NPSC2016/npsc-278.pdf