in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an...

In this study, a first-order, nonstationary stochastic model of transient flow is developed which is applicable to the entire domain of a bounded vadose zone in the presence of sink/source. We derive general equations governing the statistical moments of the flow quantities by perturbation expansions. Owing to the mathematical complexity of the equations, in general we need to solve them numeri...

The phase error in finite-difference (FD) methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy. Greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods. Both these techniques require more memory and longer computation times. In this paper, new modified methods are presented which are optimized...

The 3D Laplace equation is one of the important PDEs of physics and describes the phenomonology of electrostatics and magnetostatics. Frequently very precise solution of this PDE is required; but with conventional finite element or finite difference codes this is difficult to achieve because of the need for an exceedingly fine mesh which leads to often prohibitive CPU time. We present an altern...

The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a d...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...

Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, s...