the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...

In this paper we present a posteriori error estimators for the approximate solutions of linear parabolic equations. We consider discretizations of the problem by discontinuous Galerkin method in time corresponding to variant Crank-Nicolson schemes and continuous Galerkin method in space. Especially, £nite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson...

Abstract. We derive optimal order a posteriori error estimates for time discretizations by both the Crank–Nicolson and the Crank–Nicolson–Galerkin methods for linear and nonlinear parabolic equations. We examine both smooth and rough initial data. Our basic tool for deriving a posteriori estimates are second order Crank–Nicolson reconstructions of the piecewise linear approximate solutions. The...

and Applied Analysis 3 As in the classical Crank-Nicholson difference scheme, we will obtain a discrete approximation to the fractional derivative ∂U t, x /∂t at tn 1/2 , xi . Let H t, x 1 Γ 1 − α ∫ t 0 u s, x − u 0, x t − s α ds. 2.1

The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...

It is shown that A-acceptable and, more generally, A()-acceptablerational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.

Keywords: Benjamin–Bona–Mahony equation Method of compactness Moving boundary Crank–Nicolson method a b s t r a c t In this work we present the existence, the uniqueness and numerical solutions for a mathematical model associated with equations of Benjamin–Bona–Mahony type in a domain with moving boundary. We apply the Galerkin method, multiplier techniques, energy estimates and compactness res...

Boundary value methods are applied to find transient solutions of M/M/2 queueing systems with two heterogeneous servers under a variant vacation policy. An iterative method is employed to solve the resulting large linear system and a Crank-Nicolson preconditioner is used to accelerate the convergence. Numerical results are presented to demonstrate the efficiency of the proposed method.

To study the heat or diffusion equation it is often used the Crank-Nicolson method which is unconditionally stable and has order of convergence O(k + h ), where k and h are mesh con2 2 stants. Unfortunately, using this method in conventional floatingpoint arithmetic we get solutions including not only the method error, but also representation and rounding error, Therefore, we propose an interva...