Conservative Semidiscrete Difference Schemes for Timoshenko Systems

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that ...

Conservative finite difference schemes for the Degasperis-Procesi equation

We consider the numerical integration of the Degasperis–Procesi equation, which was recently introduced as a completely integrable shallow water equation. For the equation, we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi-Hamiltonian form of the equation at a same time. We also prove the unique solvability of the schemes, and show som...

Two Conservative Difference Schemes for the Generalized Rosenau Equation

Galilean invariance and the conservative difference schemes for scalar laws

Correspondence: [email protected]. edu.cn Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China Abstract Galilean invariance for general conservative finite difference schemes is presented in this article. Two theorems have been obtained for firstand second-order conservative schemes, which demonstrate the necessity conditions for Galilean prese...