### Abstract

A current, linear, two-dimensional mathematical model of the mechanics of the cochlea is solved numerically by using a finite difference approximation of the model equations. The finite-difference method is used to discretize Laplace's equation over a rectangular region with specified boundary conditions. The resulting matrix equation for fluid pressure is solved by using a Gaussian block-elimination technique. Numerical solutions are obtained for fluid pressure and basilar membrane displacement as a function of distance from the stapes. The finite difference method is a direct, versatile, and reasonably efficient means of solving the two-dimensional cochlear model.

Original language | English (US) |
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Pages (from-to) | 1386-1393 |

Number of pages | 8 |

Journal | Journal of the Acoustical Society of America |

Volume | 69 |

Issue number | 5 |

DOIs | |

State | Published - May 1981 |

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### ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics

### Cite this

**Finite difference solution of a two-dimensional mathematical model of the cochlea.** / Neely, Stephen T.

Research output: Contribution to journal › Article

*Journal of the Acoustical Society of America*, vol. 69, no. 5, pp. 1386-1393. https://doi.org/10.1121/1.385820

}

TY - JOUR

T1 - Finite difference solution of a two-dimensional mathematical model of the cochlea

AU - Neely, Stephen T.

PY - 1981/5

Y1 - 1981/5

N2 - A current, linear, two-dimensional mathematical model of the mechanics of the cochlea is solved numerically by using a finite difference approximation of the model equations. The finite-difference method is used to discretize Laplace's equation over a rectangular region with specified boundary conditions. The resulting matrix equation for fluid pressure is solved by using a Gaussian block-elimination technique. Numerical solutions are obtained for fluid pressure and basilar membrane displacement as a function of distance from the stapes. The finite difference method is a direct, versatile, and reasonably efficient means of solving the two-dimensional cochlear model.

AB - A current, linear, two-dimensional mathematical model of the mechanics of the cochlea is solved numerically by using a finite difference approximation of the model equations. The finite-difference method is used to discretize Laplace's equation over a rectangular region with specified boundary conditions. The resulting matrix equation for fluid pressure is solved by using a Gaussian block-elimination technique. Numerical solutions are obtained for fluid pressure and basilar membrane displacement as a function of distance from the stapes. The finite difference method is a direct, versatile, and reasonably efficient means of solving the two-dimensional cochlear model.

UR - http://www.scopus.com/inward/record.url?scp=0019461947&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019461947&partnerID=8YFLogxK

U2 - 10.1121/1.385820

DO - 10.1121/1.385820

M3 - Article

C2 - 7240568

AN - SCOPUS:0019461947

VL - 69

SP - 1386

EP - 1393

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 5

ER -