2 citations · 5 across the 15 of their papers we have counts for
15 papers
Structural Inconsistency and Stability Classification of Multi-symplectic Diamond Schemes
Kaito Sato, Shun Sato, Takayasu Matsuo
Multi-symplectic diamond schemes proposed by McLachlan and Wilkins (2015) provide a framework for the numerical integration of Hamiltonian partial differential equations, combining…
A Mathematical Analysis of a Smooth-Convex-Concave Splitting Scheme for the Swift--Hohenberg Equation
Yuki Yonekura, Daiki Iwade, Shun Sato +1
The Swift--Hohenberg equation is a widely studied fourth-order model, originally proposed to describe hydrodynamic fluctuations. It admits an energy-dissipation law and, under suit…
Essential Convergence Rates of Continuous-Time Models for Optimization Methods
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
Designing and analyzing optimization methods via continuous-time models expressed as ordinary differential equations (ODEs) is a promising approach for its intuitiveness and simpli…
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…
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…
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…
A new unified framework for designing convex optimization methods with prescribed theoretical convergence estimates: A numerical analysis approach
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept o…
Double-Exponential transformation: A quick review of a Japanese tradition
Kazuo Murota, Takayasu Matsuo
This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based metho…
Essential convergence rate of ordinary differential equations appearing in optimization
Kansei Ushiyama, Shun Sato, Takayasu Matsuo
Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODE…
On Spatial Discretization of Evolutionary Differential Equations on the Periodic Domain with a Mixed Derivative
Shun Sato, Takayasu Matsuo
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and nume…
Geometric numerical integrators for Hunter-Saxton-like equations
Yuto Miyatake, David Cohen, Daisuke Furihata +1
We present novel geometric numerical integrators for Hunter--Saxton-like equations by means of new multi-symplectic formulations and known Hamiltonian structures of the problems. W…
A self-adaptive moving mesh method for the short pulse equation via its hodograph link to the sine-Gordon equation
S. Sato, K. Oguma, T. Matsuo +1
The short pulse equation was introduced by Schaefer--Wayne (2004) for modeling the propagation of ultrashort optical pulses. While it can describe a wide range of solutions, its ul…
A novel discrete variational derivative method using "average-difference methods"
Daisuke Furihata, Shun Sato, Takayasu Matsuo
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to…
Discrete Variational Derivative Methods for the EPDiff equation
Stig Larsson, Takayasu Matsuo, Klas Modin +1
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop th…
Structure-preserving integrators for the Benjamin-type equations
Kimiaki Kinugasa, Yuto Miyatake, Takayasu Matsuo
The numerical integration of the Benjamin and Benjamin--Ono equations are considered. They are non-local partial differential equations involving the Hilbert transform, and due to…