ABSTRACT: In this article, a two-dimensional cochlear model is proposed in the time domain by using a numerical technique. The equations in this model are discretized with respect to the spatial variables by means of a method of quadrature formulas yielding a system of ordinary di erential equations in the time domain. To solve this system, a variable step size eighth-order Runge-Kutta scheme i...

A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The method uses a polynomial of one less degree than the full approximation to calculate the rst derivative so that interface values can be calculate...

The present paper analyzes the MHD effects on the steady free convective boundary layer flow of a viscous incompressible fluid over a linearly moving porous vertical semi-infinite plate with suction and viscous dissipation. The governing boundary layer equations are reduced to a two-point boundary value problem using similarity transformations. The resultant problem is solved numerically using ...

The paper deals with an approximate analysis of non-linear, non-stationary vibrational systems with multiple degrees of freedom subjected to a pulse excitation. The nonstationary system parameters, which may include masses, restoring forces or damping, are considered to be slowly varying functions of time. A general procedure for obtaining the first order approximate solution is presented throu...

Steady two-dimensional Magneto hydrodynamic free convection flow with thermal radiation in the presence of magnetic field along a vertical flat plate is concerned in the present study. The fluid is taken to be gray, absorbing-emitting radiation. The non-linear governing equations have been transformed by the usual similarity transformation to a system of ordinary differential equations. These d...

In this paper, we investigate the combined effects of buoyancy force and Navier slip on the entropy generation rate in a vertical porous channel with wall suction/injection. The nonlinear model problem is tackled numerically using Runge–Kutta–Fehlberg method with shooting technique. Both the velocity and temperature profiles are obtained and utilized to compute the entropy generation number. Th...

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full ac...

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank–Nicolson schemes can be reused for higher–order fully implicit Runge–Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order–optimal for A–stable and irreducible Runge–Kutta schemes with invertible coefficient matrices. The theoretical inv...

In this paper, we analyze second-order Runge–Kutta approximations to a nonlinear optimal control problem with control constraints. If the optimal control has a derivative of bounded variation and a coercivity condition holds, we show that for a special class of Runge–Kutta schemes, the error in the discrete approximating control is O(h2) where h is the mesh spacing.

The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...