We consider hyperbolic systems of conservation laws which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level we introduce a domain decomposition method based on an iteration-by-subdomain procedure yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The m...

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H towards a dissipative weak solution of Cam...

Abstract In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in two-dimensional domain. The space discretization is implemented by weighted shifted Grünwald (WSGD) which results stiff system of nonlinear ordinary differential equations (ODEs). This solved an efficient compact implicit integration factor (cIIF) method. stability second or...

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme...

We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order k 0 at mesh faces. The method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions. Fairly general meshes with polytopal and nonmatching cells are suppor...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.