共查询到19条相似文献,搜索用时 78 毫秒
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二维力学问题中,当有如ai(y)xi或bi(x)yi型的复杂荷载时,给出了如何将体积分近似转换为边界积分的方法. 相似文献
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讨论用配位法求一种非线性奇异积分方程的数值解。针对不同的可解条件,分别用Lagrange插值和有理插值将原方程离散为代数方程,通过求解此代数方程得到数值解和逼近解。最后将所得结果与已有的解析解的表达式进行比较。 相似文献
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随着新教材中平面区域的引进,平面区域边界方程近几年在各类考试或竞赛中频繁出现.这块内容集新颖性、综合性、探究性于一体,是训练学生思维、提高学生能力、培养学生创新意识的好素材.本文着重介绍有界平面区域的边界方程的一些求解策略,供参考. 相似文献
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刘雪丁晓王晓莹江山 《南通职业大学学报》2022,(1):56-60
考虑二维弹性力学方程,研究有限元法的有效求解,分别基于线性元和二次元基函数,对应形成稀疏程度不同的代数方程组。数值实践充分表明,有限元解有效逼近了原方程的真解,并不断减少各范数度量下的误差,其中二次元格式具有精度更好、收敛更快的对比结果。 相似文献
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基于区域分解和多项式插值,对积分算子进行离散,得到高精确度的近似离散矩阵.这一方法适应于核函数为光滑、振动较小、只有有限弱奇点的情形.如果采用n个离散点,近似矩阵可以经过O(n)次计算得到,存储也只要O(n).矩阵-向量相乘的计算量为O(nlogn).所以,此方法特别适合共轭梯度类型算法 相似文献
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马杭 《上海大学学报(英文版)》2002,6(2):101-110
With the aid of the properties of the hypersingular kernels,a geometric conversion approach was presented in this paper.The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method.Based on the conversion,the hypersingularity in the boundary integrals could be lowered by one order,resulting in the simplification of the computer code.Moreover,an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case.The approach is simple to use,which can be inserted readily to computer code,thus getting rid of the dull routine deduction of formulae before the numerical implementatins,as the expressions of these kernels are in general complicated.The numerical examples were gien in three-dimensional elasticity,verifying the effectiveness of the proposed approach,which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary. 相似文献
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通过分部积分公式及r函数的一些性质推得了向左Riemann-Liouville分数阶积分的级数表达形式.数值算例表明,用这种级数表达式做数值逼近是有效的.最后,用这种逼近方式求解一类分数阶积分微分方程. 相似文献
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The concept of eigen crack opening displacement (COD) can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an it... 相似文献
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利用Guo/Krasnoselskii不动点定理研究一类具有积分边界条件的非线性分数阶微分方程边值问题正解的存在性。 相似文献
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提出几类一阶常微分方程 ,通过变量替换法化为齐次微分方程 ,再借助交换变量位置法 ,论证它们的可积判据 ,给出它们通积分的表达式 ,所得结果是相应文献结果的推广 . 相似文献
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陈伟 《宁德师专学报(自然科学版)》2009,21(3):228-232,240
研究满足一个简单条件,但可能不满足Nagumo条件的三阶微分方程三点边值问题的微分不等式的解的存在性及其唯一性. 相似文献
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1 Introduction Theboundaryintegralequationsariseinmanyproblemsofphysicsandengineering .Oneofthepri marymathematicalandnumericaldifficultiesofboundaryintegralequationappearstobethetreat mentofthesingularkernels.Therearethreediffer enttypesofsingularities… 相似文献
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INTRODUCTION In scientific and engineering problems, Volterra integral equations are always encountered and have attracted much attention (Christopher and Baker, 1977; Delves and Mohamed, 1985; Brunner and van der Houwen, 1986; Kress, 1989; Oja and Saveljeva, 2002; Maleknejad and Shahrezaee, 2004; Maleknejad and Aghazadeh, 2005; Zerarka and Soukeur, 2005). Generally, exact solutions are very difficult to find and solutions have been obtained for only some few special cases (Yan and … 相似文献
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Zhao Zengqin 《商丘师专学报》2007,23(12):1-8
By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C^2 [ 0, 1 ] positive solutions and C^3 [ 0, 1 ] positive solutions. 相似文献
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ZHAO Zeng-qin 《商丘师范学院学报》2007,23(12):1-8
By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C2 [ 0, 1 ] positive solutions and C3 [ 0, 1 ] positive solutions. 相似文献