A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the disc...

In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility o...

in this paper, a parameter uniform numerical method based on shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. it is assumed that both equations have a turning point at the same point. an appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

an analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperaturedependent viscosity and thermal radiation on an unsteady mhd free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate by taking into account the viscous dissipation effects. the g...

In this paper we analyze an implicit finite difference scheme for the mixed initial-value Dirichlet problem for a system of two conservation laws with artificial viscosity. The system we consider is a model for'isentropic flow in one space dimension. First, we show that, under certain conditions on the mesh, the scheme is stable in the sense that it possesses an invariant set (defined by the so...

In this paper, we present an MATLAB version of a finite difference scheme for the numerical solution of the American option valuation problem. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson’s extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the optio...

Perform numerical analysis of sound generation and propagation with accuracy and with lower computational time are some of the main challenges for Computational Aeroacoustics (CAA), which had experienced some major improvements in the last decade. In the present work it was performed numerical study of two-dimensional propagation of waves by solving LEE equations applied to a Gaussian pulse in ...

in this work, we apply the radial basis functions for solving the time fractional diffusion-wave equation defined by caputo sense for                         . the problem is discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. numerical results s...

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...