The study focuses on comparing two energy-conserving schemes for the Zakharov equations: one proposed by Glassey in 1992 and another by Furihata and Matsuo in 2010. The authors prove theoretical solvability under minimal assumptions and demonstrate superior accuracy of the DVDM scheme over Glassey's linearly-implicit scheme. Despite its computational cost, the DVDM scheme shows consistent discrete conserved quantities defined at a single time step, making it advantageous. The paper provides a detailed mathematical analysis and intensive numerical experiments to compare the performance of these structure-preserving schemes.
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by Shuto Kawai,... kl. arxiv.org 03-13-2024
https://arxiv.org/pdf/2403.07336.pdfDybere Forespørgsler