欢迎您！东篱公司
退出
-
申报数据库
-
立项数据库
-
成果数据库
-
项目获奖数据库
中文摘要：
基于Duhamel项的精细积分方法,构造了几种求解非线性微分方程的数值算法。首先将非线性微分方程在形式上划分为线性部分和非线性部分,对非线性部分进行多项式近似,利用Duhamel积分矩阵,导出了非线性方程求解的一般格式。然后结合传统的数值积分技术,例如Adams线性多步法等,构造了基于精细积分方法的相应算法。本文算法利用了精细积分方法对线性部分求解高度精确的优点,大大提高了传统算法的数值精度和稳定性,尤其是对于刚性问题。本文构造的算法不需要对线性系统矩阵求逆,可以方便的考察不同的线性系统矩阵对算法性能的影响。数值算例验证了本文算法的有效性,并表明非线性系统的线性化矩阵作为线性部分是比较合理的选择。
英文摘要：
Several numerical algorithms for nonlinear differential equations are constructed based on Duhamel term＇s precise integration method（PIM）.Firstly the nonlinear differential equations are formally divided into linear and nonlinear parts and then the latter are approximated by polynomials.By applying the Duhamel integration,the general discrete forms for nonlinear differential equations are derived.Then the corresponding PIM-based algorithms are constructed by combining the traditional numerical integration techniques,such as Adams linear multi-step method,with PIM.Compared with the traditional algorithms,the new method integrates the linear part accurately by using PIM,and so improves the numerical precision and stability significantly,especially for stiff problems.Furthermore,the method proposed in this paper avoids the matrix inverse for the linear part and it is convenient to study effects of the linear matrix on the algorithm＇s performance.Numerical experiments confirmed the validity of the proposed method and show that the linearization matrix of the nonlinear system is a good choice for the linear part.
同期刊论文项目
同项目期刊论文
Roles of grain boundary and dislocations at different deformation stages of nanocrystalline copper u
Buckling behavior of carbon nanotube-based intramolecular junctions under compression: Molecular dyn
Comparison of theories for stability of truss structures Part 2: Computation of critical solution of
Combined identification of constitutive parameters and in-situ stresses for an elastic Cosserat mode
Effects of Constitutive Parameters and Dynamic Tensile Loads on Radially Periodic Oscillation of Mic
A numerical study of the imperfection effect on ultrananocrystalline diamond properties under differ
Molecular dynamics study of the specimen size and imperfection effects on the failure responses of m
A high efficient assembly technique for large proton exchange membrane fuel cell stacks: Part II App
The loading history and crystal orientation effects on the size-dependency of single crystal diamond
Simultaneous optimization of control parameters and configurations of PZT actuators for morphing str
Multiscale Model-Based Simulation with Applications to Nano and Bio Systems For the 8th World Congre
Topology optimization of continuum structures with different tensile and compressive properties in b
Solving heat transfer problems with phase change via smoothed effective heat capacity and element-fr
Equivalent analysis of orthogonal viscoelastic jointed rock via an adaptive algorithm in time domain
Penetration of Lipid Membranes by Gold Nanoparticles: Insights into Cellular Uptake, Cytotoxicity, a
Non-structure Specific Intensity Measure Parameters and Characteristic Period of Near-fault Ground M
Solving inverse couple-stress problems via an element-free Galerkin (EFG) method and Gauss-Newton al
Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellips
A study of mechanical properties of pure and nitrogen-doped ultrananocrystalline diamond films under
An investigation of combined size, rate and thermal effects on the material properties of single cry
Identification of Geometric Boundary Configurations in Heat Transfer Problems Via Element-Free Galer
Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures usin
Integrated design optimization of voltage channel distribution and control voltages for tracking the
Design of multi-tubular heat exchangers for optimum efficiency of heat dissipation Design of multi-t
Further study on efficiency of sequential approximate programming for probabilistic structural desig
A sequential approximate programming strategy for performance-measure-based probabilistic structural
Stability analyses for axially moving strings in nonlinear free and aerodynamically excited vibratio
A generalized JKR-model for two-dimensional adhesive contact of transversely isotropic piezoelectric
A new boundary search scheme for topology optimization of continuum structures with design-dependent
Recursive formulations for multibody systems with frictional joints based on the interaction between
Loading history effect on size-dependent shear strength of pure and nitrogen-doped ultrananocrystall
Coupling upscaling finite element method for consolidation analysis of heterogeneous saturated porou
New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite
A structure-preserving algorithm for the minimum H norm computation of finite-time state feedback co
位置：