Oscillation-Preserving Integrators for Second-Order ODEs with Highly Oscillatory Solutions

来源 :第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议 | 被引量 : 0次 | 上传用户：wangjie198811

【摘要】

：

　　In the last few decades,Runge-Kutta-Nystr"om(RKN) methods have made significant progress and the study of RKN-type methods for solving highly oscillatory d

【作者】

：

吴新元

【机构】

：

南京大学;曲阜师范大学

【出处】

：

第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议

【发表日期】

：

2019年8期

下载到本地 , 更方便阅读

下载此文赞助VIP

声明 : 本文档内容版权归属内容提供方 , 如果您对本文有版权争议 , 可与客服联系进行内容授权或下架

论文部分内容阅读

　　In the last few decades,Runge-Kutta-Nystr\"om(RKN) methods have made significant progress and the study of RKN-type methods for solving highly oscillatory differential equations has received a great deal of attention.

其他文献

Spectral computation of highly oscillatory integral equations in laser theory

　　We are concerned in this paper with the numerical computation of the spectra of highly oscillatory integrals that arise in laser simulations.

会议

非线性随机分数阶微分方程Euler方法的收敛性分析

　　论文首先证明了非线性随机分数阶微分方程解的存在唯一性，然后构造了数值求解该方程的Euler 方法，并证明了当方程满足一定约束条件时，该方法是弱收敛的。

会议

随机分数阶微分方程解的存在唯一性Euler方法弱收敛性Caputo导数

一类随机微分方程的指数离散梯度格式

　　本文中我们为系数中含有线性和指数成分的随机微分方程提出一类随机指数离散梯度格式，分析此类格式的根均方收敛阶，以及当它们应用于一些具有特殊结构的随机微分方程时的保

会议

随机微分方程指数积分子离散梯度方法均方收敛保结构算法

非线性波动方程组的Richardson外推法

　　本报告主要讨论了非线性波动方程组的Richardson 外推法及其收敛性。首先，运用紧致差分方法分别离散时间导数和空间导数，并引入合理的分裂项，对非线性波动方程组构造ADI 紧

会议

ADI紧致差分法Richardson外推法最大模估计收敛性

Long-time analysis of multi-symplectic numerical methods for nonlinear Dirac equations

　　In the study of symplectic integrators,long-time near-conservation of first integrals were numerically validated and rigorously analyzed by using backward e

会议

Long-time near conservationMulti-symplectic integratorsHamiltonian PDEsModula

Superconvergence and structure preservation of the collocation type exponential time integrators

　　This work is devoted to the error estimate of the collocation type exponential time integrators for solving the semilinear parabolic systems.

会议

SuperconvergenceExponential integratorStructure preservation

Multiple scalar auxiliary variables energy-preserving scheme for the Camassa-Holm equation

　　In this talk,we present a linearly implicit energy-conserving scheme for the numerical integration of the Camassa-Holm equation by using the multiple scalar

会议

MSAV approachCamassa-Holm equationenergy-preservinglinearly implicit

一类随机Volterra积分微分方程的半隐式欧拉方法的强收敛性分析

　　主要研究一类随机Volterra 积分微分方程的半隐式欧拉方法的强收敛性。通过讨论数值解的可解性和均方有界性，结合Ito 积分的性质，证明了方法的1 阶强收敛。

会议

随机Volterra积分微分方程半隐式欧拉方法有界性收敛性

Trigonometrically fitted two-derivative Runge-Kutta-Nystr(o)m methods for second-order oscillatory d

　　Order conditions for two-derivative Runge-Kutta-Nystr(o)m(TDRKN)methods are obtained via the Nystr(o)m tree theory and the B-series theory.Trigonometric fit

会议

Two-derivative Runge-Kutta-Nystr"ommethodNystr"{o}m treeB-seriesOrder conditi

Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic diff

　　In this paper,we study the linearly damped stochastic differential equations,which have the invariants satisfying a linear differential equation whose coeff

会议

Damped stochastic differential equationsConformal invariantConformal symplecti

Oscillation-Preserving Integrators for Second-Order ODEs with Highly Oscillatory Solutions

其他学术论文