Pde Definition and 743 Threads

Predicting the functional form of solution of PDE How do you conclude that the solution of the PDE u(x,y)\frac{∂u(x,y)}{∂x}+\upsilon(x,y)\frac{∂u(x,y)}{∂y}=-\frac{dp(x)}{dx}+\frac{1}{a}\frac{∂^{2}u(x,y)}{dy^{2}} is of the functional form u=f(x,y,\frac{dp(x)}{dx},a) ? I know this...

hi.. with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf page 7, “Observe” that the only way we can have formula of t only= formula of x only is for both sides to be equal to a single constant. here I do understand that for these to being equal...

I am trying to build a program in Matlab to solve the following hyperbolic PDE by the method of characteristics ∂n/∂t + G(t)∂n/∂L = 0 with the inital and boundary conditions n(t,0)=B(t)/G(t) and n(0,L)=ns Here ns is an intial distribution (bell curve) but I don't have a function to...

hello everyone i'm in my sixth semester of undergraduate physics and currently taking a math methods of physics class. So far we've been working with boundary value problems using PDE's. In the textbook we're using and from which I've been reading mostly (mathematical physics by eugene...

Homework Statement Let ##U\subset\mathbb{R}^n## be a bounded open set with smooth boundary ##\partial U##. Consider the boundary value problem $$\begin{cases}\bigtriangleup^2u=f&\text{on }U\\u=\frac{\partial u}{\partial n}=0&\text{on }\partial U\end{cases}$$where ##n## is the outward pointing...

I have a circular heat source of inner radius r1 and r2=r1+Δr on top of a pcb board. This heat source is transferring heat along the radius and the length of the beaker which is say L. I have to find temperature distribution along the length of the beaker so T(r.z). The beaker is filled with...

Homework Statement Just looking back through my notes and it looks like I'm missing some. Just a few questions. For one example in the notes I have the wave utt-c2uxx + u3 = 0 and that the energy density 1/2u2t + c2/2u2x + 1/4u4 I have that the differential form of energy conservation...

hello, guys Below is the equation I am concerned with: Is the above equation non-linear because of (delta P/delta x)^2 term assuming other variables are constant and don't change with pressure , P?

So I am currently a math undergraduate (senior though) taking an introduction partial differential equations. We are using the PDE book by Farlow (Dover reprint). It seems to be a solid book though my professor does diverge from the methods used in it fairly regularly (like not making...

(r^2 \nabla^2 - 1) X(r,\theta,z) + 2 \frac{\partial}{\partial \theta} Y(r,\theta,z) = 0 (r^2 \nabla^2 - 1) Y(r,\theta,z) - 2 \frac{\partial}{\partial \theta} X(r,\theta,z) = 0 any suggestions are greatly appreciated :)

Consider the following PDE. A lot of this is from "Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation" by J. Franklin and E. Rodemich. \frac{1}{2} \frac{\partial^2 T}{\partial y^2} + y \frac{\partial T}{\partial x} = -1 With |x|<1, |y| < \infty and we require...

I have a PDE and I have to transform it into an easier one using a substitution: u_t=u_{xx}-\beta u I am supposed to use the following substitution: u(x,t)=e^{-\beta t}w(x,t) I am supposed to get something that looks like this: w_t=w_{xx} Can someone show me the steps?

I have seen a couple of solutions to this PDE - \frac{\partial x}{\partial u}=\frac{x}{\sqrt{1+y^{2}}} One is - u=\ln \left | y+\sqrt{1+y^{2}} \right |+f\left ( x \right ) I have no idea how this is arrived at or if it's correct. This is what i want to know. The solution I've...

So there's this problem in my text that's pretty challenging. I can't seem to work out the answer that is given in the back of the book, and then I found a solution manual online that contains yet another solution. The problem is a the heat equation as follows: PDE: u_{t} = α^2u_{xx} BCs...

It's been a little too long since I've has to do this. Can someone please remind me, how do you get from: ∂u/∂t = C(∂u/∂g) to ∂^2u/∂t^2 = (C^2)(∂^2u/∂t^2) The notation here is a little clumsy, but I'm just taking the second PDE of each side. How does the C^2 get there...

Suppose we have the following IBVP: PDE: u_{t}=α^{2}u_{xx} 0<x<1 0<t<∞ BCs: u(0,t)=0, u_{x}(1,t)=1 0<t<∞ IC: u(x,0)=sin(πx) 0≤x≤1 It appears as though the BCs and the IC do not match. The derivative of temperature with respect to x at position x=1 is a constant 1...

Preface: just want to start by saying that I'm 99% sure I'm having a stability issue here in the way I'm implementing the time step since if I set \Delta t \ge 1 then for any stopping time > 1, the algorithm works as it should. For time steps smaller than 1, as the time step gets smaller and...

Homework Statement du/dt=(d^2 u)/dx^2+1 u(x,0)=f(x) du/dx (0,t)=1 du/dx (L,t)=B du/dt=0 Determine an equilibrium temperature distribution. For what value of B is there a solution? Homework Equations Not really sure what to put here. The Attempt at a Solution I started by trying to separate...

second order pde -- on invariant? What the meaning for a second order pde is rotation invariant? Is all second order pde are rotation invariant? or only laplacian?

given the heat equation \frac{\partial u}{\partial x}=\frac{\partial^2 u}{\partial x^2} what does \frac{\partial^2 u}{\partial x^2} represent on a practical, physical level? I am confused because this is not time-space acceleration, but rather a temperature-spacial derivative. thanks all!

Homework Statement I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise? Homework Equations (∂^2 T)/(∂x^2...

Hi all. I'm trying to solve this PDE but I really can't figure how. The equation is f(x,y) + \partial_x f(x,y) - 4 \partial_x f(x,y) \partial_y f(x,y) = 0 As a first approximation I think it would be possible to consider \partial_y f a function of only y and \partial_x f a function of only...

I am just wondering the author is doing in this calculation step. Given ##\displaystyle \rho A \frac {\partial^2 w}{\partial x^2} - \rho I \frac{\partial^4 w}{\partial t^2 \partial x^2} +\frac {\partial^2 }{\partial x^2}EI \frac {\partial^2 w}{\partial x^2}=q(x,t)## where ##w(x,t)=W(x)e^{-i...

Folks, Given the pde ## \displaystyle k\frac{\partial^2 T}{\partial x^2}=\rho c_0 \frac{\partial T}{\partial t}## and the BC ##T(0,t)=T_\infty## and ##T(L,t)=T_\infty## for ##t>0## and the initial condition ##T(x,0)=T_0## The author proceeds to 'normalize' the PDE in order to make the...

Hello, this is a problem I've been trying to do but I'm not sure it is right. Particularly the A_n and B_n terms. Thanks https://docs.google.com/open?id=0BwZLQ_me50B8M0sxelVrbTBhYVk

Homework Statement Hopefully no one will mind me posting this as an image. But here it is in tex: Using separation of variables, find the function u(x,t), defined for 0\leq x\leq 4\pi and t\geq 0, which satisfies the following conditions: \frac{\partial^2 u}{\partial...

Homework Statement Solve the diffusion equation: u_{xx}-\alpha^2 u_{t}=0 With the boundary and initial conditions: u(0,t)=u_{0} u(L,t)=u_{L} u(x,0=\phi(x) The Attempt at a Solution I want to solve using separation of variables... I start by assuming a solution of the form...

Hi guys! This is not a homework question, it was a question on my test a few days ago. I could not solve it. Out of memory, the problem was a rod of length L with an end fixed in a wall and the other end free. Its motion satisfies the PDE ##a^4\frac{\partial ^4 u }{\partial x^4} + \frac{\partial...

Homework Statement I must find the oscillations of a circular membrane (drum-like). 1)With the boundary condition that the membrane is fixed at r=a. 2)That the membrane is free. Homework Equations The wave equation \frac{\partial ^2 u }{\partial t^2 } - c^2 \triangle u =0...

Homework Statement A sphere of radius R at temperature T=0 is put into a bath at time t=0 whose temperature is T_0. Calculate the temperature inside the sphere \forall t \geq 0, T(\vec x ,t ). Homework Equations Heat equation: \frac{\partial T }{\partial t} \cdot \frac{1}{\kappa}...

I'm having trouble finding out how to set up Neumann (or, rather, "Robin") boundary conditions for a diffusion-type PDE. More specifically, I have a scalar function f(\boldsymbol{x}, t) where \boldsymbol{x} is n-dimensional vector space with some boundary region defined by A(\boldsymbol{x})=0...

I have a choice between 2 classes next semester that conflict, and if I choose one I will graduate without taking the other. Partial differential equations or electromagnetism? I'm a math/chemistry major and I want to go to grad school for chemical physics or physical chemistry. Any insight as...

Hi everybody, For part of my research, I need to solve an elliptic PDE like: Δu - k * u = 0, subject to : 0≤ u(x,y) ≤ 1.0 where k is a positive constant. Can anyone tell me how I can solve this problem? Thanks in advance for your help.

All, I have a system of three coupled PDE and I discretized the equations using finite difference method. It results in a block matrix equations as: [A11 A12 A13] [x1] = [f1] [A21 A22 A23] [x2] = [f2] [A31 A32 A33] [x3] = [f3] where, any of Aij is a square matrix. I use...

What are some books that are more advanced then the basic PDE books?

Hi! I am currently working with a linear PDE on the form \frac{\partial f}{\partial t} + A(v^2 - v_r^2)\frac{\partial f}{\partial \phi} + B\cos(\phi)\frac{\partial f}{\partial v} = 0. A and B are constants. I wish to find a clever coordinate substitution that simplifies, or maybe even...

Someone know how to uncouple this system of pde? Δu_{1}(x) + a u_{1}(x) + b u_{2}(x) =f(x) Δu_{2}(x) + c u_{1}(x) + d u_{2}(x) =g(x) a,b,c,d are constant. I would like to find a solution in one, two, three dimension, possibily in terms of Green function...someone could help me, please?

Dear Friends, Would you please provide me with some hints to find the analytical solution of the non-linear PDE given below: U=U(z,t) Uzz-(A/U)*Uz=Ut BC's and IC's are: U(z,0)=B U(1,t)=B Uz(0,t)=A*H(t); "H" is the heaviside function and H(0)=0 where A, B, and C are constant...

Hi, I am using the central difference method to solve a diffusion-based partial differential equation. However, my code now will not run because the time step has to be so large that Matlab cannot handle it. The large time step is due to the stability of stability: Diffusion...

$$ u(x,y) = \frac{4}{\pi}\sum_{n = 1}^{\infty}\left[\frac{\sin(2n - 1)\pi x\sinh\left[(2n - 1)\pi (1 - y)\right]}{(2n - 1)\sinh(2n - 1)\pi} + \frac{\sin(2n - 1)\pi y\sinh\left[(2n - 1)\pi(1 - x)\right]}{(2n - 1)\sinh(2n - 1)\pi}\right]. $$ How do I construct a contour plot of this?

In the course of my research I came across this PDE \frac{\partial{a_0}}{\partial{x}}\frac{\partial{a_1}}{\partial{y}}-\frac{\partial{a_0}}{\partial{y}}\frac{\partial{a_1}}{\partial{x}}=0. with both functions depending on x and y. I am quite sure I have seen equations of this form before but...

Homework Statement By trial and error, find a solution of the diffusion equation du/dt = d^2u / dx^2 with the initial condition u(x, 0) = x^2. Homework Equations The Attempt at a Solution Given the initial condition, I tried finding a solution at the steady state (du/dt=0)...

$$ \frac{1}{\alpha}T_t = T_{xx} $$ B.C are $$ T(0,t) = T(L,t) = T_{\infty} $$ I.C is $$ T(x,0) = T_i. $$ By recasting this problem in terms of non-dimensional variables, the diffusion equation along with its boundary conditions can be put into a canonical form. Suppose that we...

Hi: I have come across a PDE of the following form in my research: C_1 \alpha(t,r) + C_2 \partial_t \alpha(t,r) + C_3 \partial_r \alpha(t,r) + C_4 \beta(t,r) + C_2 \partial_t \beta(t,r) + C_3 \partial_r \beta(t,r) = 0 where the coefficients C_i are all functions of t and r: C_i =...

$$ \frac{1}{\alpha}T_t = T_{xx} $$ B.C are $$ T(0,t) = T(L,t) = T_{\infty} $$ I.C is $$ T(x,0) = T_i. $$ By recasting this problem in terms of non-dimensional variables, the diffusion equation along with its boundary conditions can be put into a canonical form. Suppose that we introduce...

I'm in truble with a partial differential equation. Actually it is a system of PDE but It would be useful to solve at least one of them. The most easy one is this one 2 \bar{\xi}\left(\bar{s},\bar{t},\bar{u}\right) - 2 \xi\left(s,t,u\right) +...

Homework Statement Check du/dt + d^2u/dx^2 + 1 = 0 Homework Equations L is a linear operator if: cL(u)=L(cu) and L(u+v)=L(u)+L(v) The Attempt at a Solution L = d/dt + d^2/dx^2 + 1 L(cu) = d(cu)/dt + d^2(cu)/dx^2 + 1 = c du/dt + c d^2(u)/dx^2 + 1 ≠ cL(u) = c du/dt + c...

Homework Statement Find the solution of yu_x + xu_y = (y-x)e^{x-y} that satisfies the auxiliary condition u(x,0) = x^4 + e^x Homework Equations Given in question The Attempt at a Solution The general solution to this is u(x,y) = f(y^2-x^2) Applying the auxiliary condition I...

Hey, I'm trying to solve the following pde, u(x,y) u_x + u_y =0 with u(x,0) = p(x) for some known p(x) where u_x defines the partial derivative of u(x,y) wrt x after finding the characteristic curves and the first integrals i get the general solution is F(x^2 - zy^2, z) = 0...

All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...