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荔园数学讲坛: Symplectic-preserving Combined High-Order Compact Scheme for Multiple Order Spatial Derivatives Differential Equations
发布时间:2022-06-20 18:22:31 1080

内容摘要: 

For differential equations with multiple order spatial derivatives, there are some shortcomings by the classical high order compact (HOC) discretization. At least one of them is to reduce the computational efficiency due to the multiple inverse manipulations of matrixes. This motivates us to design a new kind of compact method what is called combined high order compact (CHOC) methods. The basic idea lying in this kind of method is to solve all the spatial derivatives simultaneously. Then, it is used to solve coupled nonlinear Schrödinger (CNLS) equations which contain both the first and second order derivatives. This scheme is not only more compact and accurate than standard HOC scheme and standard finite difference method with the same order, but also it can construct structure-preserving schemes. It preserves the symplectic structure and mass, and sometimes energy and momentum. Numerical experiments indicate that the new scheme can simulate the CNLS equations very accurately and efficiently. The mass and momentum are exactly preserved. The energy is preserved in some especially cases.

主讲人简介: 

孔令华,教授,博士生导师,江西省百千万人才,江西省青年科学家培养对象,江西省高校学科带头人。主要研究偏微分方程的保结构算法,特别是在哈密尔顿系统高效辛和多辛格式的构造方面取得了一些研究成果,并获江西省自然科学三等奖。主持国家自然科学基金3项,江西省自然科学基金7项。发表SCI收录论文四十余篇。