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

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.