We have studied the problem of determining part of the boundary of a domain where a potential satisfies the Laplace equation. The potential and its normal derivative have prescribed values on the known part of the boundary that encloses while its normal derivative must vanish on the remaining ...
In a later chapter we will also encounter this equation (in two dimensions) as satisfied by the real and the imaginary parts of so-called analytic functions of a complex variable. The inhomogeneous equation related to the Laplace equation, called the Poisson equation, has the form (15.3)∇2...
解二维LAPLACE方程DIRICHLET问题直接边界积分方程的GALERKIN..重庆大学硕士学位论文中文摘要 摘要 Laplace方程是最典型，最简单但应用广泛的椭圆型偏微分方程。用边界元法解边值问题，由不同的边界归化方法可以得到不同的边界积分方程，数值求解边界积分方程也有好几种方法。本文考虑用Green公式和基本解推导得出直接边界积分...
Laplace's equation is reduced to solving two coupled, one-dimensional integral equations. The resulting linear equations are well-conditioned. A program package for solving Laplace's equation has been developed. The package solves Laplace's equation in two dimensions or in three dimensions with ...
theLaplaceequationisthesteady-stateheatequation.Contents1Definition2Boundaryconditions3Laplaceequationintwodimensions3.1Analyticfunctions3.2Fluidflow3.3Electrostatics4Laplaceequationinthreedimensions4.1Fundamentalsolution4.2Green'sfunction5Seealso6References7ExternallinksDefinitionInthreedimensions,theproblemistofindtwice-...
重庆大学硕士学位论文解二维Laplace方程Dirichlet问题直接边界积分方程的Galerkin边界元法姓名:***请学位级别:硕士专业:计算数学指导教师:**麟20050501更好看更何况更好看好看更好看过后付费核发规划法规和硕士论文是硕士研究生所撰写的学术论文,具有一定的理论深度和更高的学术水平,更加 硕士是一个介于学士及博士之间的研究...
Let u be a positive weak solution of equation (1.1) with finite energy, i.e.u∈D1,p(Rn):={u∈Lp⁎(Rn):∇u∈Lp(Rn)}, then u(x)=Uλ,x0(x) for some λ>0 and x0∈Rn. We mention that this result has been recently generalized in [7] in the anisotropic setting (see al...
Although here we solve the Laplace equation in two dimensions, the method is applicable to a more general class of problems. 展开 DOI: 10.1016/0021-9991(91)90242-D 年份: 1990 收藏 引用 批量引用 报错 分享 全部来源 免费下载 求助全文 Elsevier ACM ResearchGate ResearchGate (全网免费下载) ...
equation. Although the Laplace transform is named in honor of Pierre-Simon Laplace, who used the transform in his work on probability theory, the transform was discovered originally by Leonhard Euler, the prolific eighteenth-centurySwissmathematician. The Laplace transform appears in all branches of ...
andisaFredholmintegralequationofthefirstkind.ThegeneralFredholmintegralequationofthefirstkindwithlogarithmickernelin2dimensionsdoesnotalwayshaveuniquesolution,especiallyfortheunboundedproblem,itdependsontheasymptoticbehaviouratinfinity.Thesolvabilitycannotbesidestepped,foritrelatestheproblemofequivalenceofboundaryreduction....