Abstract. In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently the exact solution for the Helmholtz equation can be computed numerically. The most important features of the new schemes are that while the resulting linear system has the same simple structure as tho...

A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations...

This paper describes an alternative discretization strategy for mean-reverting models which permits the use of implicit finite difference methods along lines developed for explicit methods by Hull and White (1990a). This provides significant benefits in terms of stability, convergence, and flexibility. A technique for fitting the initial term structure is developed which is similar to that prop...

A two-dimensional (2-D) finite-difference model for elastic waves in the ground has been developed. The model uses the equation of motion and the stress-strain relation, from which a first-order stress-velocity formulation is obtained. The resulting system of equations is discretized using centered finite-differences. A perfectly matched layer surrounds the discretized solution space and absorb...

A fast approximate inversion method is proposed for the block lower triangular Toeplitz with tri-diagonal blocks (BL3TB) matrix. The BL3TB matrix is approximated by a block ε-circulant matrix, which can be efficiently inverted using the fast Fourier transforms. The error estimation is given to show the high accuracy of the approximation. In applications, the proposed method is employed to solve...

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. In this scenario the numerical schemes which preserve the discrete invariants related...

-A parallel algorithm for the class of two-point boundary value problems y" = f(z, y), y(0) = A, y(1) = B with ~ > 0 and ~ continuous on [0,1] x (—oo,oc) is presented. Using an idea similar to that in [1], we divide [0,1] into p different divisions, each division consisting of N or (N+1) (N small) unequal intervals. A high-order finite difference scheme developed for general nonuniform mesh is ...

Acoustic wave modeling is widely used to synthesize seismograms theoretically, being the basis of the reverse time migration strategy. Explicit Finite Difference Method (FDM) is often employed to find numerical solution of this problem and in this case, spatial discretization is related to the shortest wavelength to be captured and temporal discretization is determined by stability condition. I...

This paper describes a hybrid multicore/GPU solver for the incompressible Navier-Stokes equations with constant coefficients, discretized by the finite difference method. By applying the prediction-projection method, the Navier-Stokes equations are transformed into a combination of Helmholtzlike and Poisson equations for which we describe efficient solvers. As an extension of our previous paper...

We extend the Explicit Jump Immersed Interface Method (EJIIM) to stationary two phase Stokes equations with discontinuous viscosity. As the underlying finite difference method the discretization in velocity and pressure variables is used on a staggered grid. The resulting algorithm converges with second order in velocity and first in pressure. The iteration count for solving the resulting linea...