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...

This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such ...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

In this note we prove the unconditional stability of the Foschini-Miljanic algorithm. Our results show that the Foschini-Miljanic algorithm is unconditionally stable (convergent) even in the presence of bounded time-varying communication delays, and in the presence of topology changes. The implication of our results may be important for the design of Code Division Multiple Access (CDMA) based w...

We propose and analyze a linear stabilization of the Crank-Nicolson Leap-Frog (CNLF) method that removes all timestep / CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stabl...