We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H1 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 H1 towards a dissipative weak solution of C...

Ngcibi, Murali and Makamba [Fuzzy subgroups of rank two abelian$p$-group, Iranian J. of Fuzzy Systems {bf 7} (2010), 149-153]considered the number of fuzzy subgroups of a finite abelian$p$-group $mathbb{Z}_{p^m}times mathbb{Z}_{p^n}$ of rank two, andgave explicit formulas for the cases when $m$ is any positiveinteger and $n=1,2,3$. Even though their method can be used for thecases when $n=4,5,l...

Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by varying degrees of memory and computational intensity, are evaluated in the context of finite difference methods for fluid dynamics problems. It is shown that, ...

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...

We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.