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D-CONVERGENCE AND STABILITY OF A CLASS OF LINEAR multistep methods FOR NONLINEAR DDES

Journal of Computational Mathematics 2000年第2期18卷 199-206页

作者： Cheng-jian Zhang Xiao-xin Liao (Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China) 华中科技大学湖北武汉 430074

Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential eq... 详细信息

关键词： D-convergence stability multistep methods nonlinear DDEs

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High Order Semi-implicit multistep methods for Time-Dependent Partial Differential Equations

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Communications on Applied Mathematics and Computation 2021年第4期3卷 701-718页

作者： Giacomo Albi Lorenzo Pareschi Computer Science Department University of VeronaVerona 37134Italy Mathematics and Computer Science Department University of FerraraFerrara 44121Italy

We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not *** shown in Boscarino et al.(***.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative *** this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)*** findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.

关键词： Semi-implicit methods Implicit-explicit methods multistep methods Strong stability preserving High order accuracy

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IMPLICIT-EXPLICIT multistep FINITE ELEMENT-MIXED FINITE ELEMENT methods FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

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Acta Mathematica Scientia 2003年第3期23卷 386-398页

作者：陈蔚 Academy of Mathematics System science CASBeijing 100080China School of EconomicsShandong UniversityJinan 250100China

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

关键词： Semiconductor device strongly A(0)-stable multistep methods finite element methods mixed finite element methods

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BOUNDEDNESS AND ASYMPTOTIC STABILITY OFmultistep methods FOR GENERALIZED PANTOGRAPH EQUATIONS

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Journal of Computational Mathematics 2004年第3期22卷 447-456页

作者： Cheng-jianZhang GengSun DepartmentofMathematics HuazhongUniversityofScienceandTechnologyWuhan430074China InstituteofMathematicsandSystemsScience ChineseAcademyofScienceBeijing100080China

In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some ... 详细信息

关键词： Asymptotic stability Boundedness Generalized pantograph equations multistep methods

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multistep DISCRETIZATION OF INDEX 3 DAES

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Journal of Computational Mathematics 2000年第3期18卷 325-336页

作者： Yang Cao Qing-yang Li (Department of Mathematics, Tsinghua University, Beijing 100084, China) 清华大学北京 100084

Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretizati... 详细信息

关键词： multistep methods Adams method BDF DAEs Index 3

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One-Pot Synthesis of 5-Alkoxycarbonyl-4-aryl-3,4-dihydropyrimidin-2- ones Catalyzed by Phosphotungstic Acid

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有机化学 2003年第z1期23卷 93-93页

作者： JIN Tong-Shou XIAO Jin-Chong LI Tong-Shuang College of Chemistry and Environmental Science Hebei University Baoding 071002 College of Chemistry and Environmental Science Hebei University Baoding 071002 College of Chemistry and Environmental Science Hebei University Baoding 071002

　　Many dihydropyrimidinones and their derivatives play an important role in medicine due to their therapeutic and pharmacological properties. [1] They have emerged as the integral backbones of several calcium channel blockers, antihypertensive agents, alpha-1α-antagonists. [2] Strategies for the synthesis of dihydropyrimidinone nucleus have varied from one-pot to multistep approaches. Although high yields can be achieved by the following complex multistep procedures, these methods lack the simplicity comparing with Biginelli protocol which firstly reported by Biginelli by one-pot condensation of aryl aldehyde, β-ketoesters and urea with catalytic acid in 1993, and these multistep methods suffer from low yields particularly for substituted aromatic aldehyde.……

关键词： calcium channel blockers multistep methods aromatic aldehyde

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