There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of these methods preserve more than one conservation law locally. A recently-introduced strategy uses symbolic algebra to construct finite difference schemes that preserve several local conservation laws of a given scalar PDE in Kovalevskaya form. In this paper, we adapt the new strategy to PDEs that are not in Kovalevskaya form and to systems of PDEs. The Benjamin-Bona-Mahony equation and a system equivalent to the nonlinear Schroedinger equation are used as benchmarks, showing that the strategy yields conservative schemes which are robust and highly accurate compared to others in the literature.

翻译：在构建一定差异计划方面,有若干既定办法,这些办法保留了某一部分差异方程式的全球变差,然而,这些办法中很少能保留一个以上的当地养护法。最近推出的一项战略使用象征性代数来构建一定差异计划,以维护科瓦列夫斯卡亚形式的某一天际PDE的若干地方养护法。在本文件中,我们将新战略调整为非Kovalevskaya形式的PDEs和PDEs系统。本杰明-博纳-马霍尼方程式和相当于非线性施罗德因格方程式的系统被用作基准,表明与文献中的其他方案相比,该战略产生了稳健和非常准确的保守计划。