Bespoke finite difference methods that preserve two local conservation laws of the modified KdV equation
arXiv:1808.093704 citationsh-index: 10
Originality Incremental advance
AI Analysis
This work provides a method for constructing conservative numerical schemes for nonlinear wave equations, which is important for accurate long-time simulations in computational physics.
The authors developed a new class of finite difference methods for the modified KdV equation that preserve local conservation laws of mass and energy, using a symbolic-numeric approach based on discrete Euler operators.
By exploiting the fact that conservation laws form the kernel of a discrete Euler operator, we use a recently introduced symbolic-numeric approach to construct a new class of finite difference methods for the modified Korteweg-de Vries (mKdV) equation, that preserve the local conservation laws of mass and energy.