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math.NA2024
Analysis of nonquadratic energy-conservative schemes for KdV type-equations
Shuto Kawai, Shun Sato, Takayasu Matsuo
Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes…
math.NA2024
A novel interpretation of Nesterov's acceleration via variable step-size linear multistep methods
Ryota Nozawa, Shun Sato, Takayasu Matsuo
Nesterov's acceleration in continuous optimization can be understood in a novel way when Nesterov's accelerated gradient (NAG) method is considered as a linear multistep (LM) metho…
math.NA2024
Mathematical analysis and numerical comparison of energy-conservative schemes for the Zakharov equations
Shuto Kawai, Shun Sato, Takayasu Matsuo
Furihata and Matsuo proposed in 2010 an energy-conserving scheme for the Zakharov equations, as an application of the discrete variational derivative method (DVDM). This scheme is…