Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Saito, Norikazu"'
This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods
Externí odkaz:
http://arxiv.org/abs/2405.05626
The convergence properties of the upwind difference scheme for the Hamilton-Jacobi-Bellman (HJB) equation, which is a fundamental equation for optimal control theory, are investigated. We first perform a convergence analysis for the solution of the s
Externí odkaz:
http://arxiv.org/abs/2301.06415
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and it
Externí odkaz:
http://arxiv.org/abs/2204.07278
Autor:
Miyashita, Masaru, Saito, Norikazu
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a new potentia
Externí odkaz:
http://arxiv.org/abs/2201.04481
Autor:
Nakanishi, Toru, Saito, Norikazu
This study presents a new mass-lumping finite element method for computing the radially symmetric solution of a semilinear heat equation in an $N$ dimensional ball ($N\ge 2$). We provide two schemes, (ML-1) and (ML-2), and derive their error estimate
Externí odkaz:
http://arxiv.org/abs/2012.06422
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics describing the
Externí odkaz:
http://arxiv.org/abs/2004.07994
Autor:
Chiba, Yuki, Saito, Norikazu
We prove several optimal-order error estimates for a finite-element method applied to an inhomogeneous Robin boundary value problem (BVP) for the Poisson equation defined in a smooth bounded domain in $\mathbb{R}^n$, $n=2,3$. The boundary condition i
Externí odkaz:
http://arxiv.org/abs/1905.01605
Finite element method for radially symmetric solution of a multidimensional semilinear heat equation
Autor:
Nakanishi, Toru, Saito, Norikazu
This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates in $L^\inf
Externí odkaz:
http://arxiv.org/abs/1902.07919
Publikováno v:
In IFAC Journal of Systems and Control June 2023 24
Autor:
Chiba, Yuki, Saito, Norikazu
We derive several $L^\infty$ error estimates for the symmetric interior penalty (SIP) discontinuous Galerkin (DG) method applied to the Poisson equation in a two-dimensional polygonal domain. Both local and global estimates are examined. The weak max
Externí odkaz:
http://arxiv.org/abs/1812.00610