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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 494-527页

作者： Qiumei Huang Kun Jiang Jingwei Li College of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Laboratory of Mathematics and Complex Systems and School of Mathematical Science Beijing Normal UniversityBeijing 100875China

The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of *** has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation *** on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efﬁcientﬁrst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of *** analyses as well as energy stability are also *** two-dimensional and three-dimensional experiments are performed to verify these theo-retical results.

关键词： Peng-Robinson equation of state diffuse interface model maximum bound principle exponential time differencing Lagrange multiplier

STABILITY ANALYSIS AND APPLICATION OF THE exponential time differencing SCHEMES

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Journal of Computational Mathematics 2004年第2期22卷 200-209页

作者： QiangDu Wen-xiangZhu DepartmentofMathematics PennsylvaniaStateUniversityUniversityParkPA16802USA

exponential time differencing schemes are time integration methods that can be efficiently combined with spatial spectral approximations to provide very high resolution to the smooth solutions of some linear and nonlinear partial differential equations. We study in this paper the stability properties of some exponential time differencing schemes. We also present their application to the numerical solution of the scalar Allen-Cahn equation in two and three dimensional spaces.

关键词： Allen-Cahn equations Energy estimates exponential time differencing Fourier analysis Fourier spectral methods Maximum principle Phase transitions Stability time integration schemes

A LINEARLY-IMPLICIT STRUCTURE-PRESERVING exponential time differencing SCHEME FOR HAMILTONIAN PDEs

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Journal of Computational Mathematics 2024年第4期42卷 1063-1079页

作者： Yayun Fu Dongdong Hu Wenjun Cai Yushun Wang Henan Joint International Research Laboratory of High Performance Computation for Complex Systems School of ScienceXuchang UniversityXuchang 461000China School of Mathematics and Statistics Jiangxi Normal UniversityJiangxiNanchang 330022China Jiangsu Key Laboratory for NSLSCS Jiangsu Collaborative Innovation Center of Biomedial Functional MaterialsSchool of Mathematical SciencesNanjing Normal UniversityNanjing 210023China

In the paper,we propose a novel linearly implicit structure-preserving algorithm,which is derived by combing the invariant energy quadratization approach with the exponential time differencing method,to construct efficient and accurate time discretization scheme for a large class of Hamiltonian partial differential equations(PDEs).The proposed scheme is a linear system,and can be solved more efficient than the original energy-preserving ex-ponential integrator scheme which usually needs nonlinear *** experiments are performed to verify the conservation,efficiency and good performance at relatively large time step in long time computations.

关键词： Structure-preserving algorithm Hamiltonian PDE Energy quadratization method exponential time differencing

Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and exponential time differencing Schemes for the Thin Film Epitaxy Problem without Slope Selection

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Advances in Applied Mathematics and Mechanics 2023年第3期15卷 545-567页

作者： Danni Zhang Ruihan Guo School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China

In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope *** relax the severe time step restriction of explicit time marching methods,we employ a class of exponential time differencing(ETD)schemes for time integration,which is based on a linear convex splitting *** experiments of the accuracy and long time simulations are given to show the efficiency and capability of the proposed numerical schemes.

关键词： Local discontinuous Galerkin method thin film epitaxy problem error estimates exponential time differencing long time simulation

Localized exponential time differencing Method for Shallow Water Equations: Algorithms and Numerical Study

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Communications in Computational Physics 2021年第1期29卷 80-110页

作者： Xucheng Meng Thi-Thao-Phuong Hoang Zhu Wang Lili Ju Department of Mathematics University of South CarolinaColumbiaSC 29208USA Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China Center for Mathematical studies Advanced Institute of Natural SciencesBeijing Normal University at ZhuhaiZhuhaiGuangdong 519087China

In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water *** with explicit time stepping of the same order accuracy in time,the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical *** accelerate the ETD simulations,we propose a localized approach that synthesizes the ETD method and overlapping domain *** dividing the original problem into many subdomain problems of smaller sizes and solving them locally,the proposed approach could speed up the calculation of matrix exponential vector *** standard test cases for shallow water equations of one or multiple layers are *** results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

关键词： exponential time differencing domain decomposition rotating shallow water equa-tions finite volume discretization

An ETD Method for American Options under the Heston Model

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Computer Modeling in Engineering & Sciences 2020年第8期124卷 493-508页

作者： Rafael Company Vera N.Egorova Lucas Jódar Ferran Fuster Valls Instituto de Matemática Multidisciplinar Universitat Politècnica de ValènciaValencia46022Spain Depto.de Matemática Aplicada y Ciencias de la Computación Universidad de CantabriaSantander39005Spain Nfoque Advisory Services Madrid28001Spain

A numerical method for American options pricing on assets under the Heston stochastic volatility model is developed.A preliminary transformation is applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational *** boundary is treated by the penalty *** nonlinear partial differential equation is solved numerically by using the method of *** full discretization the exponential time differencing method is *** analysis establishes the stability and positivity of the proposed *** numerical convergence behaviour and effectiveness are investigated in extensive numerical experiments.

关键词： Heston model American option pricing exponential time differencing semi-discretization