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...

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 propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

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...

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...

Lattice Boltzmann schemes rely on the enlargement of size target problem in order to solve PDEs a highly parallelizable and efficient kinetic-like fashion, split into collision stream phase. This structure, despite well-known advantages from computational standpoint, is not suitable construct rigorous notion consistency with respect equations provide precise stability. In alleviate these shorta...