Article history: Received 24 March 2015 Received in revised form 25 September 2015 Accepted 1 November 2015 Available online 4 November 2015

Many musical instruments have interfaces which emphasise the pitch of the sound produced over other perceptual characteristics, such as its timbre. This is at odds with the musical developments of the last century. In this paper, we introduce a method for replacing the interface of musical instruments (both conventional and unconventional) with a more flexible interface which can present the in...

We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa– Holm equation ut−uxxt +3uux−2uxuxx−uuxxx = 0 with initial data u|t=0 = u0 ∈ H1([0, 1]). Here it is assumed that u0 − u′′ 0 ≥ 0 and in this case, the solution is unique, globally defined, and energy preserving.

In this paper, we provide stability and convergence analysis for a class of finite difference schemes for unsteady incompressibleNavier-Stokes equations in vorticity-stream function formulation. The no-slip boundary condition for the velocity is converted into local vorticity boundary conditions. Thom’s formula, Wilkes’ formula, or other local formulas in the earlier literature can be used in t...

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

We consider the stability of a finite difference scheme with two weight parameters for a hyperbolic equation with nonlocal integral boundary conditions. We obtain stability region in the complex plane by investigating the characteristic equation of a difference scheme using the root criterion.

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed.The difference scheme simulates two conservative quantities of the problemwell.The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditi...

In this work, we propose a model of nonlocal partial differential equation (PDE) with deviated type function in the boundary condition. This model is solved numerically by finite difference method (FDM) using variable space grid (VSG) technique. The results obtained by this method are in a good agreement with the solution of the corresponding rectangular domain problem. Also, we investigated th...