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We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev\u2013Petviashvili equation.<\/jats:p>","DOI":"10.1007\/s10208-021-09511-1","type":"journal-article","created":{"date-parts":[[2021,5,19]],"date-time":"2021-05-19T20:02:20Z","timestamp":1621454540000},"page":"477-506","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A New Technique for Preserving Conservation Laws"],"prefix":"10.1007","volume":"22","author":[{"given":"Gianluca","family":"Frasca-Caccia","sequence":"first","affiliation":[]},{"given":"Peter E.","family":"Hydon","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,19]]},"reference":[{"key":"9511_CR1","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1111\/sapm.12174","volume":"139","author":"A Ankiewicz","year":"2017","unstructured":"A.\u00a0Ankiewicz, A.\u00a0P.\u00a0Bassom, P.\u00a0A.\u00a0Clarkson and E.\u00a0Dowie, Conservation laws and integral relations for the Boussinesq equation, Stud. 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