Pde Definition and 856 Threads

Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} = \frac{dU}{U-1} Solving the first and third gives: \frac{U-1}{x} = c_1 The...

Homework Statement Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Homework Equations The Attempt at a Solution Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} =...

I am solving the following simple looking nonlinear PDE: (\partial f / \partial t)^2 - (\partial f / \partial r)^2 = 1 Using different tricks and ansatzs I've obtained the following analytic solutions so far: f(r,t) = a\, t + b\, r + c, \,\,\,\, a^2 - b^2=1. f(r,t) =...

Hey everyone, I'm a rising junior scheduled to take a Methods of Mathematical Physics class this coming fall. I've heard that this class utilizes a lot of partial differential equations, and I'd like to get a bit of a jumpstart and familiarize myself with some concepts before the semester...

The ONLY solution of PDE: f_t g_r = f_r g_t ? I have the following PDE: \frac{\partial f(r,t)}{\partial t} \, \, \frac{\partial g(r,t)}{\partial r} = \frac{\partial f(r,t)}{\partial r} \, \, \frac{\partial g(r,t)}{\partial t} By a simple check, I know a solution is f = h(g), where h() is...

Homework Statement oh! after trying to re-solve a PDE I reached this: Homework Equations \sum\frac{4}{((2n-1)\pi)^2} (a+\frac{4(-1)^{n+1}}{(2n-1)\pi}) cos(\frac{2n-1}{2}\pi x) n goes feom 1 to \infty and "a" is a constant value. The Attempt at a Solution the solution i am...

For an elliptic PDE Uxx + Uyy + Ux + Uy = -1 in D = {x^2 + y^2 = 1} and U = 0 on the boundary of D = {x^2 + y^2 = 1} is it possible for me to make a change of variables and eliminate the Ux and Uy and get the Laplace equation Uaa + Ubb = 0? I tried converting into polar coordinates, but the...

(partial derivatives didn't carry over well, so I just used a d) Homework Statement Give an example (as simple as possible) of a reference temperature distribution r = r(x, t) satisfying the following boundary conditions DN: r(0, t) = A(t), (dr(L,t) / dx) = B(t); NN: (dr(0,t) / dx) =...

Use the Laplace transform to solve \frac{\partial^2 y }{ \partial t^2 } = c^2 \frac{ \partial^2 y }{ \partial x^2 } for x>0, t>0 y(0,t) = t, for t>0 y(x,0) = 0, \frac{\partial y(x,0) }{ \partial t } = A, for x>0So I used the Laplace transform of a derivative, along with the initial conditions...

Homework Statement Does anyone know of how to proove that the solution of the differential equation u_{t} = u_{xx} is f(x+t)+ g(x-t) in general functions. Homework Equations The Attempt at a Solution It is a pretty easy problem for normal functions, but i have no clue of how to...

[b]1. We look at a Laplace equation ( \Delta u(x,y) =o) on a square [0, 1]* [0, 1] If we know that u_{x=o}= siny , u_{x=1}= cosy u_y|_{y=0}= 0 , u_y|_{y=1}= 0 we differentiate here by y. proove that |u|<=1. The Attempt at a Solution We now know that the maximum of u has to be...

Homework Statement u*u_x + y*u_y = xInitial condition: u = 2*s on the parametric curve given by x = s, y = s, s is any real number. Homework Equations Given the equation: a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z) Here, u(x,y) is an unknown function which we're trying to find...

Homework Statement U is a function of x and t d/dt(U) = d/dx(U) + V(x,t)U U(x,0) = f(x) Suppose: U(x,t) = e^(Integral from 0 to 1 [V(x+s,t-s)]ds) * f(x+t) Show directly (no change of variables) that this solves the above PDE Show using change of variables that this solves the...

Hi all, Homework Statement Determine the equilibrium temperature distribution (if it exists). For what values of B, are there solutions. Homework Equations a) Ut = Uxx + 1, U(x,0) = f(x), Ux(0,t) = 1, U(L,t) = B b) Ut = Uxx + X - B, U(x,0) = f(x), Ux(0,t) = 0, U(L,t) = 0 The...

Hi! If you don't see clearly this n terms please download the word file attached here. Am a given a problem like f(x,y,y')= y''= x+y with y(0)=0, y'(0)=1 and h=0.1 and i want to solve it using Ringe Kutta. As we know y_(n+1)= y_n + h(y'_n+(A_n + B_n + C_n)/3) And y'_(n+1) =...

It is a 1-D wave equation problem with fixed ends, no initial velocity, and initial displacement of 2sin(\pi x) on the interval 0<x<4, t>0. See my attached documents of my work. I end up with a c_n value of 0 based on the integration. I am pretty confident I set up the problem correctly as it...

Homework Statement Solve the following IVP for 1st order quasilinear PDE s using the method of characteristics. u*u_x + y*u_y = x u = 2s, y = s, x = s Homework Equations a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z) z = u(x_o,y_o) = 2s The Attempt at a Solution The...

Hi, I'm looking over the examples in my book for this problem and the general approach is a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z) where u(x,y) I have the following problem in my notes: 1/x * u_x + 1/y * u_y = x^2 * sqrt(z) and I get the solution easily because of the format...

My PDE book does the following: \int \phi_x^2 dx Where, \phi_x = b-\frac{b}{a} |x| for |x|> a and x=0 otherwise. Strauss claims: \int \phi_x^2 dx = ( \frac{b}{a} ) ^2 2a However, I think there is a mistake. It can be shown that: \frac{-3a}{b}(b-...

[SOLVED] Seperation of variables - first order PDE Homework Statement I have the expression X'(x)/X(x) = cx. How do I separate the variables? It's the fraction on the left side that annoys me. I know that X'(x) = d(X(x))/dx, but I can't use this here? EDIT: Sorry for the mis-spelled title...

Homework Statement In this problem I'm trying to derive an explicit solution for Langmuir waves in a plasma. In part (a) of the problem I derived the wave equation (\partial_t_t+\omega_e^2-3v_e^2\partial_x_x) E(x,t) = 0 This matches the solution in the book so I believe it's correct...

[SOLVED] transforming a parabolic pde to normal form Homework Statement The problem is to transform the PDE to normal form. The PDE in question is parabolic: U_{xx} - 2U_{xy} + U_{yy} = 0 but I also need to solve other problems for hyperbolic pde's so general advice would be appreciated...

Hello everybody, I have a problem here related to QFT in a research project. I end up with some Dirac equation with space-time dependent mass in 2 spatial dimensions. More mathematically, the PDE to solve is \left( {i\left( {\sigma ^i \otimes I_2 } \right)\partial _i + g_y \varphi...

Homework Statement Does anyone know how to solve this PDE for u:R-->R and some initial conditions? u_{xy}=ku where k is a positive constant. Or this one, also for u:R-->R and some initial conditions: u_{tt}=u_{xx}-Ku where K is a positive constant.The Attempt at a Solution I can solve the...

Is there any established theory concerning infinite dimensional PDE?

PDE with boundary conditions Full question A function u(x,y) has two independent variables x and y and satisfies the 1st order PDE x \frac{du}{dx} - \frac{y}{2}\frac{du}{dy}= 0 by first looking for a separable solution u(x,y)=X(x)Y(y), find the general solution of the equation. determine...

First post, hooray! Undergrad nuke engineer here, trying to figure out a really annoying PDE. My notation for U_xx = 2nd partial of U with respect to x, U_tt = 2nd partial of U with respect to t, etc. Homework Statement I'm working a nonhomogenous PDE with homogeneous initial and boundary...

There is a theorem (the "Borel lemma") that says: Let (A_n) by any sequence of real numbers. We can built a function "F", indefinitely differentiable, such that if G is the n-derivative of f, G(0) = a_n. Does someone knows a proof or where can I find it? The theorem appears in wikipedia...

Hello In our math course, we encountered the following elliptic PDE: y^{2}u_{xx} + u_{yy} = 0 In order to solve it, we converted it to the characteristic equation, y^{2}\left(\frac{dy}{dx}\right)^{2} + 1 = 0 Next, we wrote: \frac{dy}{dx} = \frac{i}{y} My question is...

pde involving airy function! If u(x,t) satisfies ∂u/∂t + ∂³u/∂x³ = 0, with u(x,0) = f(x), and u, ∂u/∂x, ∂²u/∂x² -> 0 as |x| -> ∞, use Fourier transform methods to show that u(x,t) = (3t)^(-1/3) ∫f(y) Ai[(x-y)/((3t)^(-1/3))] dy (integral from -∞ to ∞), where Ai(x) is the Airy function, for...

The question is: Write a short paragraph that physical problem modeled by the equation: \frac{\partial{U}}{\partial{t}} = \frac{1}{4}\frac{\partial^2{U}}{\partial^2{x}} -12[U - 8x] Subject to IC: U(x,0) = 3x BCs: U(0,t) =0, u(2,t) = 2t Okay so clearly, the physical problem is...

I know how to do differential equations and a plot a phase plane with pplane7. But I have no clue how to do the same for pde's. Is it similar or not at all?

PDE is type of heat equation. Many book only gives an example of solving heat equation using Fourier transform. An exercise asks me to solve it for using Fourier and laplace transform: In the heat equation, we'd take the Fourier transform with respect to x for each term in the equation...

hello! does anyone know how to solve the following (like an eigenvalue) PDE with matlab? aFxx+bFx+cFyy+dFy+eFxy=\lambda*F in which i am solving F with certain boundary conditions and a,b,c,d,e are functions independent of F. "pdeeig" in MATLAB doesn't seem to be able to handle...

Homework Statement I would like to know how to solve the PDE \frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}+\frac{\partial f}{\partial z}=g(x,y,z) * f is the unknown function * g(x,y,z) is a known and smooth function Homework Equations divf=g The Attempt...

How do I transform a second-order PDE with constant coefficients into the canonical form? I tried to solve this problem: u_xx + 13u_yy + 14u_zz - 6u_xy + 6u_yz + 2u_xz -u_x +2u_y = 0 I wrote the bilinear form of the second order derivatives and diagonalized it. I found out that it is a...

Homework Statement Consider \nabla ^2 u = Q\left( {x,y,z} \right) in the half space region z > 0 where u(x,y,o) = 0. The relevant Green's function is G(x,y,z|x',y',z'). Find the solution to the PDE in terms of G. If Q\left( {x,y,z} \right) = x^2 e^{ - z} \delta \left( {x - 2}...

Homework Statement I have a problem that I'm trying to make sense of. Note y_t is the partial derivative of y with respect to t and y_tt is the second order partial derivative of y with respect to t, etc. The complete problem statement is the following: Show that for the equation...

Need urgent help on laplace transform and PDE ! I'm stuck with this 2 questions ... q1) Using laplace transforms, solve: y" + 4y = r(t), where r(t) = {3sint, 0<t<pi, -3sint, t>pi y(0)=0, y'(0)=3. this is what i get after rewriting for the step function: 3sint [1-u(t-pi)] + (-3sint)u(t-pi)...

What exactly is a smooth solution to PDEs. I couldn't find the definition in my books, googled that and came up empty handed. I suspect the solution must be continuous with all the deriviatives.

Homework Statement Find the PDE for this general solution: U(x,y) = Phi(x+y) + Psi(x-2y) Homework Equations The Attempt at a Solution I let my xi = x+y and my eta = x-2y and found that both roots are {-1,1/2}. From that I multiplied: (dy/dx - root1)*(dy/dx - root2) to give me the...

I have got a heat flow partial differential equation problem that is giving me a little problem due to the direction the temperature is changing. I have a bar (which lies along the X axis) which is initially at a uniform temperature which (for simplicity sake) we will call zero degrees. At...

Homework Statement \frac{{\partial u}}{{\partial t}} = \frac{{\partial ^2 u}}{{\partial x^2 }} + 1,0 < x < \infty ,t > 0 Let \xi = \frac{x}{{\sqrt t }} and write u = t^b f\left( \xi \right). Determine the value of b required for f\left( \xi \right) to satisfy an ordinary...

I would really like to know whether initial conditions given to a time evolution PDE has to satisfy the governing equations. For example, if I have to solve numerically an incompressible flow equation do I need to give initial solution for the velocity field which is divergence free so as to...

Homework Statement Show that the first order derivative y'(xi) in the point xi may be approximated by y'(xi)= (1/12*h) * (-3yi-1 -10yi + 18yi+1 -6yi+2 + yi+3) - (1/20h) h^4*y^(5) + O(h^5) The Attempt at a Solution I think the idea is to setup a linear system and some how use taylor...

A trick on PDE?? Hi all. I am reading a text in mathematical wave theory. I saw and am confused by a manipulation of a PDE, as shown in the attached figure. I don't really undertand how the equation (1.9) is transformed by "introducing the charcteristic variables). (as indicated by the red...

I have just started to study PDE myself. Could anyone tell me some websites and/or materials that can help me in learning.

Hi Solving a Killing vector problem, in General Relativity, I got the following PDE system: \frac{\partial X^0}{\partial x}=0 \frac{\partial X^1}{\partial y}=0 \frac{\partial X^2}{\partial z}=0 \frac{\partial X^0}{\partial y} + \frac{\partial X^1}{\partial x}=0 \frac{\partial...

How do you solve this simple PDE? D/Dr (f) = D/Dt (f) ? Pls don't just give me the final answer.

Crank-Nicolson method for solving hyperbolic PDE? Hi. I'm not really sure if this is the right part of the forum to ask since it's not really a home-work "problem". Anyway, the question seemed too trivial to ask in the general math forum. What I'm wondering is wether the Crank-Nicolson...