Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
SIAM Journal on Scientific Computing
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Fast simulation of solid tumors thermal ablation treatments with a 3D reaction diffusion model
Computers in Biology and Medicine
Fast numerical solution of nonlinear nonlocal cochlear models
Journal of Computational Physics
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The interest of inner ear research towards the cochlear simulation is due to the lack of imaging techniques for human noninvasive investigation. Unfortunately, in case of Sensorineural Hearing Loss (SHL), the majority of the models developed in the literature do not take into consideration all the complex audiological phenomena occurring in the Organ of Corti. In this paper we show that a realistic analysis of recruitment and hyperacusis can be effectively reproduced by nonlinear modeling. The latter fact is in contrast to the classical assumption that an impaired ear with a moderate SHL can be effectively described by a passive linear model. In order to deal with the active role performed by the Outer Hair Cells (OHC), recent models based on integro-differential equations were introduced in the literature. However, the discretization and the computational methods present some issues. In this work we suggest the utilization of a variable-step-variable order package to advance in time in order to preserve the character of the continuous solution. Moreover, we illustrate that, in case of SHL, the fixed-point approach for the linear algebraic system generated by the discretization can be inappropriate. Since preliminary experiences show that the matrices involved in the model present clustered eigenvalues, we propose Krylov methods. Numerical tests are included in order to confirm the effectiveness of the proposal.