Numerical preservation of multiple local conservation laws
作者：
Highlights：
• A novel strategy that uses symbolic algebra to find finite difference methods that preserve conservation laws is applied to the Benjamin-Bona-Mahony (BBM) equation and to the nonlinear Schroedinger (NLS) equation.
• New parametrized families of conservative numerical schemes are introduced for each of these equations.
• For the NLS equation, we derive also new time integrators of the Ablowitz-Ladik model that preserve multiple conservation laws.
• For various benchmark problems, we find members in each new family of schemes that give very accurate solutions compared to other schemes from the literature.
摘要
•A novel strategy that uses symbolic algebra to find finite difference methods that preserve conservation laws is applied to the Benjamin-Bona-Mahony (BBM) equation and to the nonlinear Schroedinger (NLS) equation.•New parametrized families of conservative numerical schemes are introduced for each of these equations.•For the NLS equation, we derive also new time integrators of the Ablowitz-Ladik model that preserve multiple conservation laws.•For various benchmark problems, we find members in each new family of schemes that give very accurate solutions compared to other schemes from the literature.
论文关键词：Finite difference methods,Discrete conservation laws,BBM equation,Nonlinear Schrödinger equation,Energy conservation,Momentum conservation
论文评审过程：Received 24 September 2020, Revised 11 March 2021, Accepted 13 March 2021, Available online 26 March 2021, Version of Record 26 March 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126203
