The family of the KdV equations, the most famous equations embodying both nonlinearity and dispersion, has attracted enormous attention over the years and has served as the model equation for the development of soliton theory. In this paper we present a comparative study between two different methods for solving the general KdV equation, namely the numerical Crank Nicolson method, and the semi-...

Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of such coupled problems can be computationally expensive, we consider loosely-coupled and stronglycoupled solution algorithms in which higher order multi-stage Runge-Kutta schemes are employed for time integration. The higher order time i...

• We discretize the 2D peridynamics equation using a time Crank-Nicolson/spatial asymptotically compatible scheme. The boundary conditions prevent. corner reflections for peridynamics. numerical stability condition is proven. aim of this paper to construct accurate absorbing (ABCs) two-dimensional motion which describes nonlocal phenomena arising in continuum mechanics based on integrodifferent...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable. Keywords—Generalized Rosenau-B...

We interpret the Cayley transform of linear (finiteor infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. If such a scheme is applied to a conservative system, then the resulting discrete time system is conservative in the discrete time sense. We show that the convergence of this integration scheme is equivalent to an approximation of the Laplace ...

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the ...

This paper adresses the construction and study of a Crank-Nicolson-type discretization of the two-dimensional linear Schrödinger equation in a bounded domain Ω with artificial boundary conditions set on the arbitrarily shaped boundary of Ω. These conditions present the features of being differential in space and nonlocal in time since their definition involves some time fractional operators. Af...

The time dependent transport equation is solved with stabilized continuous, piecewise linear finite elements and the Crank-Nicolson scheme [1]. Finite elements with large aspect ratio are advocated in order to account for boundary layers. The error due to space discretization has already been studied in [2]. Here, the error due to the use of the Crank-Nicolson scheme is taken into account. Anis...