Sixth-order symmetric and symplectic exponentially fitted Runge–Kutta methods of the Gauss type

AbstractThe construction of exponentially fitted Runge–Kutta (EFRK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. Based on the symplecticness, symmetry, and exponential fitting properties, two new three-stage RK integrators of the Gauss type with fixed or variable nodes, are obtained. The new exponentially fitted RK Gauss type methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt),exp(−λt)}, λ∈C, and in particular {sin(ωt),cos(ωt)} when λ=iω, ω∈R. The algebraic order of the new integrators is also analyzed, obtaining that they are of sixth-order like the classical three-stage RK Gauss method. Some numerical experiments show that the new methods are more efficient than the symplectic RK Gauss methods (either standard or else exponentially fitted) proposed in the scientific literature

Exponentially-fitted methods and their stability functions

Is it possible to determine the stability function of an exponentially-fitted Runge-Kutta method, without actually constructing the method itself? This question was answered in a recent paper and examples were given for one-stage methods. In this paper we summarize the results and we focus on two-stage methods

エネルギー関数を持つ発展方程式に対する幾何学的数値計算法

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 松尾 宇泰, 東京大学教授 中島 研吾, 東京大学准教授 鈴木 秀幸, 東京大学准教授 長尾 大道, 東京大学准教授 齋藤 宣一University of Tokyo(東京大学