Pde Definition and 857 Threads

Hello! I am trying to solve the following second order PDE (copy that into mathematica): \!\( \*SubscriptBox[\(\[PartialD]\), \(x, t\)]\(\[Delta][x, t]\)\) + b \!\( \*SubscriptBox[\(\[PartialD]\), \(t\)]\(\[Delta][x, t]\)\) + a \!\( \*SubscriptBox[\(\[PartialD]\), \(\(x\)\(\...

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 Solve: PDE: 9Uxx=Utt BC: U(0, t) = U(∏, t) = 0 IC: U(x, 0) = sin4x + 7sin5x Ut = x 0 < x < ∏/2 = ∏ - x ∏/2 < x < ∏ Homework Equations Fourier Sine Series and Cosine Series Equations The Attempt at a Solution...

Homework Statement Solve: ∂u/∂t = k ∂2u/∂x2 - ζu with the initial condition u(x,0) = f(x) where k and ζ are constants. x is on an infinite domain.Homework Equations Define Fourier transforms: f(x) = ∫[-∞,∞]F(w)e-iwxdw F(w) = 1/2∏ ∫[-∞,∞]f(x)eiwxdxFrom tables of Fourier Transforms...

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...

Since the hurricane has killed school for awhile, I was working on some stuff that I knew we would not cover in class any more, but could end up on a test and I got to this question. It seems like it should be simple, but I have been stumped all day. Don't know if anyone here will have the...

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...

Hi, I'm really interesting of PDE, but I don't really know what I have to learn before start with PDE. I have learn multivariable calculus and ODE, but are there something need to learn before PDE? Thanks in advance.

Hi, Say I have this pde: u_t=\alpha u_{xx} u(0,t)=\sin{x}+\sin{2x} u(L,t)=0 I know the solution for the pde below is v(x,t): v_t=\alpha v_{xx} v(0,t)=\sin{x} v(L,t)=0 And I know the solution for the pde below is w(x,t) w_t=\alpha w_{xx} w(0,t)=\sin{2x} w(L,t)=0 Would...

Hi Everyone, I was reading a paper and I found it hard to comprehend how some of the equations were arrived at, probably because my math rottenness. Anyway I need your help on understanding how these equations were arrived at. The problem goes like this: We have this PDE in cylindrical...

Homework Statement Solve u_t -k u_xx +V u_x=0 With the initial condition, u(x,0)=f(x) Use the transformation y=x-Vt Homework Equations The solution to the equation u_t - k u_xx=0 with the initial condition is u(x,t)=1/Sqrt[4\pi kt] \int e^(-(x-y)^2 /4kt)f(y) dy The Attempt at a...

In my research work, I recently have come across a system of three linear first order pde's whose characteristic polynomial has one real and two complex conjugate zeros. I have searched the available resources and could nowhere find out which category (elliptic/hyperbolic/parabolic) it falls...

I was looking through a calculus book doing some of the practice problems where I was asked to calculate the curl of a few functions. One of them got me thinking, is there a function whose curl is itself? Much like how e^{x} is it's own derivative, is there a vector field that is it's own curl...

anyone have any ideas on a technique to tackle this PDE: u_{tt} = u_{xx} + u_{xxxx} its like a 4th order wave equation any help or references would be appreciated

Homework Statement Consider the PDE which has the solution The Attempt at a Solution So what I am having trouble is solving it using this method. I am going to say that my $$u(x,t) = \sum_{n=1}^{\infty} u_n(t) \sin(nx)$$ and $$x \sin(t) =...

Hi!This is a quite sophisticated problem, but it’s interesting and challenging! Consider the following case: Let’s say we have a 3-dimensional disk with a radius r_{2} and a thickness d (so it actually is a cylinder with a quite short height compared to radius). We’re interested in solving...

I just graduated with a B.S. Math and Physics Minor. I took Probability but not Statistics. I also didn't get a chance to take PDE. I'm looking for some good textbooks on the subjects.

Hi, I have an equation of the form; \frac{d}{dt}(W) = \omega \left(x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) W + g \frac{\partial}{\partial y} W + k x \frac{\partial^2}{\partial y^2} W I want to change it into the rotating frame using the transform; x...

Homework Statement Given a positive subharmonic function u , defined on R^2 , how can I prove that u[ /itex] must be constant? Homework Equations \Delta u \leq 0 is the definition of subharmonic function ! The Attempt at a Solution I've tried solving this by using a new...

Hi all! I'm stuck with a system of PDE. I'm not sure I want to write it here in full, so l'll write just one of them. I've found a solution to this equation but I'm not sure it's the most general one since when I plug this solution into the other eqs, I get a trivility condition for the...

Hi all, I have a system of 3 coupled linear PDEs which can be expressed in matrix form as: \left( \begin{array}{ccc} \alpha_1 \partial_{\theta} & \alpha_2 & \alpha_3 \\ \beta_1 \partial_r & \beta_2 & \beta_3 \\ 0 & \gamma_2 \partial_{\theta} & 1 + \gamma_3 \partial_r \\ \end{array}...

Homework Statement solve x2ux + y2uy = 0 for u(2,y) = y Homework Equations The Attempt at a Solution with a = x2 and b = y2 y' = b/a = (y/x)2 this can be solved for y by separation of variables: y = \frac{x}{1-xC} and C = \frac{y-x}{xy} now u(x,y) = f(C) = f(\frac{y-x}{xy}) applying...

Hi, my equation is; \frac{\partial}{\partial t}U(x,y,t) = 2g \left( x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) U(x,y,t) I want to find the general solution to this but I don't know how to find it? Any help would be great...thanks :D

I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations. Thank you