共查询到20条相似文献，搜索用时 31 毫秒
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A modified Lindstedt-Poincaré(LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equations are converted into a group of linear ordinary differential equations by introducing a set of simple transformations.An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modified method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation,and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales. 相似文献
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古传运 《乐山师范学院学报》2014,(5):5-7
研究了一类非线性分数阶两点边值问题。利用广义的凹算子的不动点定理和格林函数的性质及在给定的条件下,获得了此边值问题正解的存在唯一性,并构造一迭代序列去逼近它。完善和推广了正解的存在性结果。 相似文献
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ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｒｅｃｅｎｔｙｅａｒｓ,ｏｒｔｈｏｇｏｎａｌｐｏｌｙｎｏｍｉａｌｓａｎｄｆｕｎｃｔｉｏｎｓｄｅｖｅｌｏｐｅｄｂｙＣｈａｎｇｅｔａｌ.( 1 986)ｈａｖｅｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙａｐｐｌｉｅｄｉｎｔｈｅｆｉｅｌｄｏｆｄｙｎａｍｉｃｓｙｓｔｅｍｓ,ｆｏｒａｎａｌｙｓｉｓａｎｄｉｄｅｎｔｉｆｉｃａｔｉｏｎｏｆｌｉｎｅａｒｓｙｓｔｅｍｓａｎｄｔｈｅｏｐｔｉｍａｌｃｏｎｔｒｏｌ (Ｔｓａｙｅｔａｌ.,1 987) .Ｔｈｅｍａｉｎａｄｖａｎｔａｇｅｏｆｔｈｉｓｔｅｃｈｎｉｑｕｅｉｓｔｈｅ… 相似文献
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As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases. 相似文献
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Based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for the bending of nonlinear viscoelastic beams was established in this paper. The Laplace transformation method and the Titchmarsh theorem were used to prove that some relations exist between solutions to bending problems of visco- and elastic beams, which reveals the fugue effect of viscoelastic materials. The high-order Galerkin approximate solution to the quasi-static response of nonlinear viscoelastic beams under a step load was obtained by using the new method suggested in this paper as well as the Mathematica software and the Newton iteration technique. 相似文献
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主要研究了一类变系数二阶非线性常微分方程的边界层问题。先确定边界层的位置,然后用匹配渐近展开法来求得该问题的一阶近似解。 相似文献
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研究一种具有多个决策者卷入,各决策者的目标不止一个,决策者之间存在二阶递阶关系系统--双层多目标规划问题.给出双层多目标决策问题数学模型的一种解决方法,把线性加权模理想点法和Kuhn-Tucker条件结合起来,从而把双层多目标规划问题转化为单层单目标约束规划问题,进而求得原问题的满意有效解. 相似文献
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应用拉格朗日方程,得到了柴油机轴系受简谐力作用的非线性振动微分方程。根据非线性振动的多尺度解法,求得系统满足1/3次亚谐共振情况的一次近似解,并对其进行数值计算。给出了1/3次亚谐共振存在区域,并分析外激励、调谐值、阻尼等对系统的影响。最后建立Simulink模型进行仿真分析。 相似文献
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讨论一类概周期系数非线性方程,就其概周期解的存在性、唯一性、稳定性等问题与线性方程系进行比较研究.通过证明发现非线性系具有线性方程系的4条主要性质,且证明了在小指数扰动情况下,非线性系的概周期解仍然保持渐近稳定. 相似文献
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借助Fischer函数将凸多面体上的垂直线性互补问题(VLCP)等价地转化为一个非线性方程组系统,在较弱条件下,给出了VLCP的误差界;同时,给出了一种求解VLCP的Levenberg-Marquardt方法,并在不要求存在非退化解的条件下证明了这种方法的全局收敛性和二次收敛性. 相似文献
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对于求解线性规划问题提出了一个基于尺度中心路径的预估-矫正光滑化方法.在适当的假设条件下,证明了方法的全局和局部二次收敛性.特别,在方法的局部二次收敛性分析中,不需要假定线性规划的解是唯一的.文中的方法可以推广到P0-线性互补问题和单调线性互补问题. 相似文献
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Michael J. Kolen 《Journal of Educational Measurement》1988,25(2):97-110
Scale scores for educational tests can be made more interpretable by incorporating score precision information at the time the score scale is established. Methods for incorporating this information are examined that are applicable to testing situations with number-correct scoring. Both linear and nonlinear methods are described. These methods can be used to construct score scales that discourage the overinterpretation of small differences in scores. The application of the nonlinear methods also results in scale scores that have nearly equal error variability along the score scale and that possess the property that adding a specified number of points to and subtracting the same number of points from any examinee's scale score produces an approximate two-sided confidence interval with a specified coverage. These nonlinear methods use an arcsine transformation to stabilize measurement error variance for transformed scores. The methods are compared through the use of illustrative examples. The effect of rounding on measurement error variability is also considered and illustrated using stanines 相似文献
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给出了线性定常系统存在加权和的Liapunov函数的条件和零解稳定性的一些新的实用判别法,将有关结果推广到线性时变系统;讨论了非线性系统的相应线性化问题． 相似文献
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MO Guo-liang ZHAO Ya-nan 《浙江大学学报(A卷英文版)》2006,7(12):2043-2049
INTRODUCTION B-spline curves and surfaces have been widely used in Computer Graphics (CG) and Computer Aided Design (CAD) (Hoschek and Lasser, 1993; Piegl and Tiller, 1997). Many practical algorithms, such as those for position and derivatives evaluation, knot insertion, knot deletion and degree elevation, are usually implemented in a CAD system that uses B-spline as a shape design tool. In curve and surface design, a given B-spline curve or surface usually needs to be extended in … 相似文献
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从理论上给出了高维非线性映射的替代型求法,并给出了在奇点的线性项可对角化的映射的规范型求法。该方法是构造性的,具有相当的适用性,同时给出了两个例子。 相似文献
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李宝凤 《唐山师范学院学报》2014,(2):1-6
给出了基于 Bernstein多项式求解分数阶微分方程的配置方法。首先,在 Bernstein级数的截断式中用tα（0〈α〈1）代替t得到分数阶Bernstein级数截断式,采用Caputo分数阶导数构建分数阶Bernstein级数截断式的矩阵形式。其次,把方程中的每一项用分数阶Bernstein级数截断式转换成矩阵形式,选取配置点,得到相应于非线性代数方程的基本矩阵方程。最后得到由条件矩阵形式和基本矩阵方程构成的新方程组,其解给出了截断项为N的近似解,同时给出了基于残余函数的误差分析。举例说明了这种方法的有效性和可行性。 相似文献
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韩金春 《连云港师范高等专科学校学报》2005,(4):64-66
给出一个求广义强非线性拟变分不等式分歧值近似解的迭代算法，谊算法不同于文[1]中的算法，进一步证明近似解序列强收敛于精确解。 相似文献