Some classification results for hyperbolic equations F(x, y, u, u(x), u(y), u(xx), u(xy), u(yy))=0 Method of laplaceF-gordon equationsLineal second-order scalar hyperbolic equations in the planeDescribe pseudospherical surfacesNonlinear-wave equationsDarboux... M Juras - 《Journal of ...
The semi-linear equation uxx uyy = f(x, y, u) with Dirichlet boundary conditions is solved by an O(h4) finite difference method, which has local truncation error O(h2) at the mesh points neighboring the boundary and O(h4) at most interior mesh points. It is proved that the...
偏微分方程是一种含有未知函数及其各阶偏导数的方程，如ut－a2(uxx+uyy+uzz)＝0（1），其中u＝u(x,y,z,t)为未知函数，x、y、z、t是自变量。18世纪时，数学家们已经开始利用偏微分方程来研究各种问题。方程（1）可以用来描述热传导规律。1746年，J.LeR.达朗贝尔给出了一维波动方程，描述了两端...
Question: Solve the Laplace equation uxx + Uyy = 0 over the square region with boundary conditions, u(0,y) = 0 and u(3,y) = 6 + y for 0 sy s3; u(x,0) = 2x and u(x, 3) = x2 for 0 sy s3 with h = 1 By performing tw...
解空间是五维的。有拉普拉斯方程可以推出A=－C。由于u=Ax²+Bxy+Cy²+Dx+Ey+F。一次项和交叉项求两次导都为零了。只有Ax²和Cy²项，然后可以得到A+B=0。故u=A(x²－y²)+Bxy+Dx+Ey+F。其中有五个自由变量，A，B，D，E，F。x²－y²，...
Dirichlet, Neumann, and mixed boundary value problems for the wave equation uxx - uyy = 0 for a rectangle. Appl. Anal. 1971;1:1-12.Abdul-Latif, A., & Diaz, J. B. (1971). Dirichlet, Neumann, and mixed boundary value problems for the wave equation uxx - uyy = 0 for a ...
Group properties of uxx −umyuyy =f(u) 来自 Elsevier 喜欢 0 阅读量: 17 作者: DJ Arrigo 摘要: The group properties and the associated Lie algebra are developed for the named quasilinear equation, for arbitrary m and f where m∈R, m≠0, f∈C2(R), f\́ne 0. From the resulting...
U = ln(x²+y²) , Uxx和Uyy 分别是 U 对x和y的二阶偏导数 Ux = (2x) /(x²+y²)Uxx = 2[ (x²+y²) - x * 2x ] / (x²+y²)² = 2(y²- x²) / (x²+y²)²Ux = (2y) /(x&...
5.考察由下列定解问题uxx +uyy =0,u(O,y)=0,u(a,y)=O,u(x,O)=f(x), u(x,b)=0,描述的矩形平板 (0≤x≤a,0≤y≤b) )上的温度分布,其中f(x)为已知的连续函数. 相关知识点: 试题来源: 解析 sinh nπ(b-y) sin1=2/(sinπ/(sin))sina/(sinb)⋅sina/a . 5.u(...
ut－a2（uxx＋uyy＋uzz）＝0（1）其中u＝u（x，y，z，t）为未知函数 ，x ，y，z，t 是自变 量。18 世纪 ，数学家们已开始用偏 微分方程来研究问题 。方程（1）便是用来描述热的传导规律的。1746年 ，J.LeR.达朗贝尔给出了一维波动方程（两端固定的弦的振动问题）：由于弦的两端固定，故...