检索结果-内蒙古大学图书馆

implicit-explicit methods based on strong stability preserving multistep time discretizations

APPLIED NUMERICAL MATHEMATICS 2007年第8期57卷 911-919页

作者： Gjesdal, Thor Norwegian Def Res Establishment NO-2027 Kjeller Norway

In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their properties with respect to the implicit and explicit eigenvalues. One of the proposed schemes is found to have very good stability properties, with implicit A-stability for the entire explicit stability domain. The properties of the other proposed schemes are comparable to those of traditional methods found in the literature. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： implicit-explicit methods strong stability preserving methods advection-diffusion equation stability

来源：评论

学校读者我要写书评

暂无评论

implicit-explicit MULTISTEP methods FOR HYPERBOLIC SYSTEMS WITH MULTISCALE RELAXATION

引用

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2020年第4期42卷 A2402-A2435页

作者： Albi, Giacomo Dimarco, Giacomo Pareschi, Lorenzo Univ Verona Comp Sci Dept Verona Italy Univ Ferrara Dept Math & Comp Sci I-44121 Ferrara Italy

We consider the development of high-order space and time numerical methods based on implicit-explicit multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which the convection and the source term may have very different time and space scales. As a consequence, the nature of the asymptotic limit changes completely, passing from a hyperbolic to a parabolic system. From the computational point of view, standard numerical methods designed for the fluid-dynamic scaling of hyperbolic systems with relaxation present several drawbacks and typically lose efficiency in describing the parabolic limit regime. In this work, in the context of implicit-explicit linear multistep methods we construct high-order space-time discretizations which are able to handle all the different scales and to capture the correct asymptotic behavior, independently from its nature, without time step restrictions imposed by the fast scales. Several numerical examples confirm the theoretical analysis.

关键词： implicit-explicit methods linear multistep methods hyperbolic balance laws fluid-dynamic limit diffusion limit asymptotic-preserving schemes

来源：评论

学校读者我要写书评

暂无评论

Dispersion-Preserving implicit-explicit Numerical methods for Reactive Flow Models

引用

INTERNATIONAL JOURNAL OF COMPUTATIONAL methods 2024年第3期21卷

作者： Amikiya, Emmanuel A. Banda, Mapundi K. Univ Pretoria Dept Math & Appl Math Private Bag X20 ZA-0028 Hatfield South Africa

Chemical reactions occur everywhere in both natural and artificial systems. Some of the reactions occur during the flow of a fluid (such a process is referred to as a reactive flow). Given the hazardous nature of some reactive flows, computer simulations (rather than physical experiments) are necessary for ascertaining or enhancing our understanding of such systems. The process of simulation involves mathematical and numerical modeling of the reactive flows. Mathematical models for reactive flow problems are complicated partial differential equations that often lack exact solutions, thus, numerical solutions are employed. Numerical methods must preserve almost all the relevant properties of the problem for accuracy reasons. Dispersion relations are important properties of wave propagation problems and numerical methods that satisfy them are called dispersion preserving methods. Furthermore, stiff transport models are wave propagation problems that cannot be solved efficiently with explicit methods. However, fully implicit methods are computationally expensive. A combination of implicit and explicit methods called implicit-explicit methods is usually employed to efficiently resolve stiffness. An example of problems of interest in this regard are the advection-diffusion-reaction (ADR) models. In this discussion, spectral analysis is performed on two implicit-explicit methods to ascertain their dispersion preserving abilities in order to determine their suitability for simulating general stiff reactive flow problems. The analysis shows that both implicit-explicit methods are dispersion preserving, however, one particular method is more suitable for general wave propagation problems.

关键词： Reactive flow spectral analysis dispersion relations wave propagation problems implicit-explicit methods

来源：评论

学校读者我要写书评

暂无评论

Analysis for implicit and implicit-explicit ADER and DeC methods for ordinary differential equations, advection-diffusion and advection-dispersion equations

引用

APPLIED NUMERICAL MATHEMATICS 2025年 212卷 110-134页

作者： Oeffner, Philipp Petri, Louis Torlo, Davide Johannes Gutenberg Univ Mainz Inst Math Staudingerweg 9 D-55128 Mainz Germany Tech Univ Clausthal Inst Math Clausthal Zellerfeld Germany Univ Roma Sapienza Dipartimento Matemat Guido Castelnuovo Rome Italy

In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a focus on their stability analysis both as solvers for ordinary differential equations (ODEs) and within the context of linear partial differential equations (PDEs). To analyze their stability, we reinterpret these methods as Runge-Kutta schemes and uncover significant variations in stability behavior, ranging from A-stable to bounded stability regions, depending on the chosen order, method, and quadrature nodes. This differentiation contrasts with their explicit counterparts. When applied to advection-diffusion and advection-dispersion equations employing finite difference spatial discretization, the von Neumann stability analysis demonstrates stability under CFL-like conditions. Particularly noteworthy is the stability maintenance observed for the advectiondiffusion equation, even under spatial-independent constraints. Furthermore, we establish precise boundaries for relevant coefficients and provide suggestions regarding the suitability of specific schemes for different problem.

关键词： implicit-explicit methods Deferred correction ADER Stability Advection-diffusion Advection-dispersion

来源：评论

学校读者我要写书评

暂无评论

implicit-explicit Runge-Kutta methods for pricing financial derivatives in state-dependent regime-switching jump-diffusion models

引用

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2024年第2期70卷 1601-1632页

作者： Maurya, Vikas Singh, Ankit Rajpoot, Manoj K. Rajiv Gandhi Inst Petr Technol Dept Math Sci Math & Comp Lab Amethi 229304 UP India

In this paper, we have devised a novel class of implicit-explicit Runge-Kutta methods for the valuation of financial derivatives under state-dependent regime-switching jump-diffusion models. The developed methods utilize an implicit technique to solve the problem without performing inversion of the coefficient matrix at each state of the economy. The pricing of European options under the regime-switching jump-diffusion process is formulated by coupled partial integro-differential equations, whereas the pricing framework for American options is based on addressing coupled linear complementary problems. The operator splitting technique is employed along with implicit-explicit methods to solve the linear complementarity problems. Consistency and convergence results of the developed methods are theoretically established using the discrete l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell <^>implicit-explicit methods$$\end{document}-norm. The accuracy and efficiency of developed methods are validated by solving the European and American options at different states of the economy under regime-switching jump-diffusion models. Finally, the computed results are compared with the recently proposed methods mentioned in the literature.

关键词： Regime-switching process Partial integro-differential equations implicit-explicit methods Operator splitting Stability analysis European and American options

来源：评论

学校读者我要写书评

暂无评论

implicit-explicit MULTIRATE INFINITESIMAL GARK methods

引用

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2021年第5期43卷 A3082-A3113页

作者： Chinomona, Rujeko Reynolds, Daniel R. Southern Methodist Univ Math Dallas TX 75275 USA

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified "fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge-Kutta (IMEXMRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

关键词： multirate time integration implicit-explicit methods multirate infinitesimal step multiple time stepping ordinary differential equations

来源：评论

学校读者我要写书评

暂无评论

Comparison of implicit-explicit and Newton linearized variable two-step BDF methods for semilinear parabolic equations

引用

COMPUTATIONAL & APPLIED MATHEMATICS 2023年第1期42卷 1-20页

作者： Wang, Wansheng Jin, Chengyu Huang, Yi Li, Linhai Zhang, Chun Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Hunan Normal Univ Coll Informat Sci & Engn Changsha 410081 Peoples R China

It is interesting to compare implicit-explicit (IMEX) and Newton linearized (NL) methods since they are two classes of typical time discretization methods for solving nonlinear differential equations. In this paper, we compare IMEX with NL two-step backward differentiation formula (BDF2) methods with variable step-size for solving semilinear parabolic differential equations. Under the appropriate time-step ratio restriction, the stability of the two methods is established by energy estimates and recent novel technique. Based on these stability results, the a priori error bounds for these methods are also derived. Numerical results not only illustrate the feasibility of the proposed method for solving semilinear parabolic differential equations but also reveal that IMEX BDF2 method is more effective than NL BDF2 method.

关键词： Semilinear parabolic equations Variable step-sizes BDF methods implicit-explicit methods Newton linearized methods Stability Error estimates

来源：评论

学校读者我要写书评

暂无评论

A CLASS OF implicit-explicit TWO-STEP RUNGE-KUTTA methods

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2015年第1期53卷 321-341页

作者： Zharovsky, Evgeniy Sandu, Adrian Zhang, Hong Tech Univ Munich Chair Numer D-85748 Garching Germany Virginia Tech Dept Comp Sci Sci Computat Lab Blacksburg VA 24061 USA

This work develops new implicit-explicit time integrators based on two-step Runge-Kutta methods. The class of schemes of interest is characterized by linear invariant preservation and high stage orders. Theoretical consistency, stability, and stiff convergence analyses are performed to reveal the excellent properties of these methods. The new framework offers extreme flexibility in the construction of partitioned integrators since no coupling conditions are necessary. Practical schemes of orders three, four, and six are constructed and are used to solve several test problems. Numerical results confirm the theoretical findings.

关键词： implicit-explicit methods two-step Runge-Kutta order reduction

来源：评论

学校读者我要写书评

暂无评论

On the stability of implicit-explicit linear multistep methods

引用

APPLIED NUMERICAL MATHEMATICS 1997年第2-3期25卷 193-205页

作者： Frank, J Hundsdorfer, W Verwer, JG CWI P.O. Box 94079 1090 GB Amsterdam The Netherlands

In many applications, such as atmospheric chemistry, large systems of ordinary differential equations (ODEs) with both stiff and nonstiff parts have to be solved numerically. A popular approach in such cases is to integrate the stiff parts implicitly and the nonstiff parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linear stability of popular second order methods like extrapolated BDF, Crank-Nicolson leap-frog and a particular class of Adams methods. We present results for problems with decoupled eigenvalues and comment on some specific CFL restrictions associated with advection terms. (C) 1997 Elsevier Science B.V.

关键词： implicit-explicit methods linear multistep methods method of lines stability

来源：评论

学校读者我要写书评

暂无评论

Highly stable implicit-explicit Runge-Kutta methods

引用

APPLIED NUMERICAL MATHEMATICS 2017年 113卷 71-92页

作者： Izzo, Giuseppe Jackiewicz, Zdzislaw Univ Naples Federico II Dipartimento Matemat & Applicaz R Caccioppoli I-80126 Naples Italy Arizona State Univ Dept Math Tempe AZ 85287 USA AGH Univ Sci & Technol Krakow Poland

We investigate implicit-explicit (IMEX) Runge-Kutta (RK) methods for differential systems with non-stiff and stiff processes. The construction of such methods with large regions of absolute stability of the 'explicit part' of the method assuming that the 'implicit part' of the scheme is A-stable, is described. We also describe the construction of IMEX RK methods, where the 'explicit part' of the schemes have strong stability properties. Examples of highly stable IMEX RK methods are provided up to the order p = 4. Numerical examples are also given which illustrate good performance of these schemes. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Runge-Kutta methods implicit-explicit methods Stability analysis Strong stability preserving Courant-Friedrichs-Levy condition Hyperbolic conservation laws

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：