1. B

    Applying Boundary Conditions

    Hi Can someone explain to me how the particular solution was derived from the boundary conditions, ie how the xe^(2(x-1)) was derived. Kind regards Beetle
  2. X

    volume of solid bounded by boundary

    I was told to find the volume of solid above z = (x^2) + (y^2) and below x-y plane , but the shaded region provided by author is above x-y plane and below z = (x^2) + (y^2) , am i correct ?
  3. X

    boundary condition

    can someone explain what dies u mean ? in the ans given , u(0, t) = 0 , and also u(10, t) = 0 ? in the lower part , i was also told that at t= 0 , u =1 , du/ dt = x i'm confused at t = 0 , u = 0 or u = 1 ???
  4. M

    Find the boundary condition of the nonlinear partial differential equations

    I have first-order nonlinear partial differential equations \frac{du}{dt}+u\frac{du}{dx} =-u^3, u\Bigr|_{t=0}=f(x) solution dt=\frac{dx}{u}=-\frac{du}{u^3} F(x-\frac{1}{u},t-\frac{1}{2u^2}) Need find boundary conditions f(x) (for example u(t=0,x)=x and find $u$) But my simple function have a...
  5. W

    Nonlinear boundary problem: counterexample

    Hi! Maybe someone can come up with any idea about this. Let us assume nonlinear two-point boundary problem x''=f(t,x,x') with boundary conditions written as L_1(x(a),x(b),x'(a),x'(b))=0, L_2(x(a),x(b),x'(a),x'(b))=0, where f\in C([a,b]\times R^2,R) and L_1,L_2\in C(R^4,R). Further assume that...
  6. W

    Boundary and initial value

    Working on some review my teacher posted and I can't seem to figure out where she got w(0) = -0.1 from. Thank you
  7. S

    Rayleigh-Ritz Method for Plate Buckling Boundary Value Problem

    Hello Everybody, I need some help if possible for the following problem. I want to calculate the deflection formula and the critical buckling load for a rectangular composite plate under uniaxial in plane load. The plate is clamped on the loaded ends and free on the unloaded...
  8. M

    Analytical Solution to 1D Heat Equation with Neumann and Robin Boundary Conditions

    Hello, I'm modeling the 1D temperature response of an object with an insulated and convection boundary conditions. Consequently, I'm looking for the solution for the 1D heat equation with neumann and robin boundary conditions, but I can't seem to get a hold of it, despite my arduous search. I'm...
  9. L

    How do I find signal to noise boundary of a decaying Signal

    Hi, I need to find the noise boundary in a Free induction decay. I can acquire an independent measure of the noise. A free induction decay starts in time with a lot of signal and as time goes by the signal fades into noise. I can't use a t test because I don't have a random group of...
  10. B

    Put up linear equation system for boundary value problem

    For \Omega = (0,1) \subseteq \mathbb R^2, f \in C(\Omega) consider the boundary value problem: - \Delta u(x,y) + u(x,y) = f(x,y)~ \forall (x,y) \in \Omega \\ u(0,y)=u(1,y) ~ \forall y \in (0,1) \\ u(x,0)= u(x,1) ~ \forall x \in (0,1) For discretization: n \in \mathbb N, h= 1/n, x_i = (i-1)...
  11. S

    Is a closed surface boundary of a handlebody?

    Hi; I have a question: If a closed surface is embedded in 3-sphere, then does it bounds a handlebody? If so, how to prove it. Thank you in advance
  12. A

    Poisson equation with three boundary conditions

    I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions...
  13. Educated

    Complex analysis, show max |f(z)| + |g(z)| is on the boundary

    So in the textbook, it starts by assuming that it doesn't take on its maximum on the boundary and then finding a contradiction. So there must be some point z_0 not on the boundary such that |f(z_0)| + |g(z_0)| takes on its maximum. Then this is where I get confused: Let f (z_0) = Ae^{-i...
  14. V

    Solution to Laplace equation with simple boundary conditions

    Hi, I've been learning how to use the 2D Laplace equation recently. I have problem concerning electric fields and I found this explanation - where the boundary conditions are the same as mine - V = 1 for x = 0 V = 0 for y = 0 V = 0 for y = 100...
  15. Z

    Lagrange multipliers for Neumann-type boundary conditions

    I would like to solve the biharmonic equation \Delta^2 u=f(x,y) on [-1,1]\times[-1,1] with u=\frac{\partial u}{\partial n}=0 on the boundary. I applied the weak form and then used Legendre-Galerkin spectral method. The Dirichlet condition u=0 can easily be incorporated but what about the other...
  16. G

    Boundary integral method to solve poisson equation

    Suggest how to solve Poisson equation \begin{equation} σ ∇^2 V = - I δ(x-x_s) δ(y-y_s) δ(z-z_s) \nonumber \end{equation} by using the boundary integration method to calculate the potential $V(r,z)$ with the help of changing the Poisson equation into cylindrical polar co ordinates? Where V is...
  17. S

    Please help! Using finite difference scheme, approximate the solution of boundary vp

    Hi guys. Morning. well I'm sooo stuck on this question. Any help would be grate. thanks in advance (Rofl) Question: Consider the boundary value problem with p(x)=1, q(x)=1.30765, and r(x)=cos(x) on [0,pi/2]. Where Alpha =-0.3 and Beta=-0.1. Using the finite-difference scheme and a hand...
  18. M

    Calculating the boundary conditions of a differential equation

    Hi, I am doing a problem and need help... I am really confused :/ Well, the problem says "Show that the boundary conditions for zZ''(z)+Z'(z)+v^2Z(z)=0 are |Z(0)|<\infty and Z(L)=0 (we know that v>0)." Z(z) comes from y(z,t)=Z(z)T(t). This problem is about the dynamic behaviour of a hanging...
  19. A

    Is wave and heat equation with zero boundary a Poisson Equation?

    I have two questions: (1)As the tittle, if u(a,\theta,t)=0, is \frac{\partial{u}}{\partial {t}}=\frac{\partial^2{u}}{\partial {r}^2}+\frac{1}{r}\frac{\partial{u}}{\partial {r}}+\frac{1}{r^2}\frac{\partial^2{u}}{\partial {\theta}^2} and \frac{\partial^2{u}}{\partial...
  20. M

    Boundary value problem

    I have the following problems to solve: The temperature u(r) in the circular ring shown in the image is determined from the boundary-value problem where u0 and u1 are constants. Show that Not sure where to start. I need to show and...