A New Technique for Preserving Conservation Laws

Abstract This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of given PDE that preserve multiple local conservation laws. We prove one spatial dimension, various one-step time integrators from the literature fully discrete laws whose densities are either quadratic or Hamiltonian. The approach generalizes to with more steps and other kinds; higher-dimensional PDEs can be treated by iterating strategy. use Boussinesq equation as benchmark introduce families schemes order two four three show technique is practicable dependent variables, introducing an example second-order potential Kadomtsev–Petviashvili equation.