Pde Definition and 743 Threads

Hi, I am currently taking a class which is now covering PDE's and I think I need more sample or example problems that are already solved, particularly on Fourier series solution, d'Alembert method, etc. The book I'm using is Kreyszig, Advanced Engineering Mathematics, 9th edition. Are...

Solve u_{xx}-3u_{xt}-4u_{tt}=0 with initial conditions u(x,0)=x^2, u_t(x,0)=e^x. I got that u is an arbitrary function F(x+t), which makes no sense. I factored the operator into (\partial/\partial x+\partial/\partial t)(\partial/\partial x-4\partial/\partial t)u=0, but I can't get anywhere.

How does this method work? What are the mathematical ideas behind this method? Unlike separation of variables techniques, where things can be worked out from first principles, this method of solving ODE seems to find the right formulas and apply which I feel uncomfortable about.

hmmm i have no idea where to even start with this problem, i cannot find any examples that are similar or anything like that anywhere! http://img147.imageshack.us/img147/2319/picture18ur9.png anyone got an idea as to a good first step to take? thanks sarah :) edit: i tryed something wild...

Hi all, I am stuggling with this question ... http://img86.imageshack.us/img86/2662/picture6fb5.png so far i have only tried part (a), but since i can't see how to do that so far... :( ok so what to do... do we first look at an 'associated problem' ? ... something like...

Hi everyone, I'm having a bit of trouble with this pde problem: http://img243.imageshack.us/img243/9313/picture3ui3.png i get the answer to be u(x,t)=0 but i am guessing that's not right. is the general solution to this problem: u(x,t) = f(x+ct) + g(x-ct) ?? thanks sarah :)

Hi can someone please help me work through the following question. It is the two dimensional Laplace equation in a semi-infinite strip. \frac{{\partial ^2 u}}{{\partial x^2 }} + \frac{{\partial ^2 u}}{{\partial y^2 }} = 0,0 < x < a,0 < y < \infty The boundary conditions along the...

I've searched through about 5 math books but don't know how to start this one: I have a drumskin of radius a, and small transverse oscillations of amplitude: \nabla^2 z = \frac{1}{c^2}\frac{\partial^2 z }{dt^2} Ok, so I can write the normal mode as z=Z(\rho)cos(\omega t)...

i want to understand finite element method by solving the simple differential equation of falling mass d2y/dx2=force/mass eventhough this equation contains derivative of only one variable i want to understand fem using this Or some one can give a somemore difficult pde and solve using...

case 1)in finite element analysis of structures using simple rod elements we do the stiffness matrix and then find the displacements from loads and constraints case 2)finite element method is a technique for solving partial differential equations. In the case1 what is the partial...

As part of a separable solution to a PDE, I get the following ODE: X''-rX=0 (*), with -infty<x<infty and the boundary condition X(+/-infty)=0 (X is an odd function here). Thus I have assumed r>0 to avoid the periodic solution, cos. I, therefore, argue that the solution is the symmetric...

Lets say we have a solution u, to the cauchy problem of the heat PDE: u_t-laplacian(u) = 0 u(x, 0) = f(x) u is a bounded solution, meaning: u<=C*e^(a*|x|^2) Where C and a are constant. Then, does u is necesseraly the following solution: u = integral of (K(x, y, t)*f(y)) Where K...

I have to give a 35-50 minute presentation on PDEs in a week and a half for my class. I really don't have much knowledge of PDE's and I was wondering if anyone knew of any good internet rescourses etc. that would help me get a decent grasp so that I could make a decent presentation and answer a...

I have a square area with the length a. The temperature surrounding the square is T_0 except at the top where it's T_0(1+sin(pi*x/a)). They ask for the stationary temperature in the area. In other words, how can the temperature u(x,y) inside the area be written when the time = infinity. The...

hello i am trying to find the fundamental solution to \frac{\partial c}{\partial t} = D\frac{\partial ^2 c}{\partial x^2} where c=c(x,t) with initial condition being c(x,0)=\delta (x) where \delta (x) is the dirac delta function. i have the solution and working written out in front of me...

u_{a}+u_{t}=-\mu t_{u} u(a,0)=u_{0}(a) u(0,t)=b\int_0^\infty \left u(a,t)da Solve u(a,t) for the region a<t Got this question from assignment. My solution is incomplete though, need some inspirations! I have shown that the general solution is u(a,t)=F(a-t)e^{-1/2{\mu}t^{2}} So for...

hi, i am having difficulty trying to find a change of variables to solve this partial differential equation \frac{\partial f}{\partial t} = t^\gamma \frac{\partial ^2 f}{\partial x^2} not sure how to pluck out a change of variables by looking at the equation as its definitely not obvious to the...

Plz Help :( Hi I want 2 know how 2 solve 1st order partial differintial equation (PDE) with constant coefficient using orthogonal transformation example : solve: 2Ux + 2Uy + Uz = 0 THnx :blushing:

A quick question: When classifying a 2nd order PDE as either Hyperbolic, Parabolic or Elliptic we look at whether the discriminant is either positive, zero or negative respectively. Right. What do we do if the discriminant depends on independent variables (or the dependent variable for that...

I have a problem that I tried to solve using MAPLE but I guess wasnt doing the right thing. \frac {\partial ^{2} \delta}{\partial t^{2}}+ S*(\frac {\partial^{2}\delta}{\partial \eta^{2}}+M*\frac {\partial^{4}\delta}{\partial \eta^{4}})-G* \frac {\partial ^{3} \delta}{\partial \eta ^{2}...

Hi, I'm working through 'Partial Differential Equations, an introduction' by Colton and am not finding it as clear as I hoped to. I'm working through an example on how to solve a linear 1st order PDE. I'll post Colton's example and Italic my questions: Find the GS of xu_x-yu_y+u=x...

What's the best exposition of Partial Differential Equations methods at the beginning-graduate level? I've found myself needing Green's functions and such and I don't really know that much about them. Dover reprints would be awesome. Thanks!

Find u(3/4,2) when l=c=1, f(x) = x(1-x), g(x) = x^2 (1-x) all i need to do is find the value using d'Alembert's solution of the one dimensional wave. now it is easy for me to extend f(x) for f(x) (-1,0)\Rightarrow \quad x(1+x) (0,1)\Rightarrow \quad x(1-x) (1,2)\Rightarrow \quad...

Let's say I assumed that the answer to a PDE was U(x,t)= XT, where X,T are functions. I then further my answer by getting to a point for T'/T=kX''/X, where k is some constant given in the boundary conditions. I then continue by working on either side to find each function. Suppose I work on...

we are given the laplacian: (d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's u=0 for (-1<y<1) on x=0 u=0 on the lines y=plus or minus 1 for x>0 u tends to zero as x tends to infinity. Using separation of variable I get the general solution u =...

I am to reduce the following PDE to 2 ODEs and find only the particular solutions: u_tt - u_xx - u = 0; u_t(x,0) = 0; u(0,t) = u(1,t) = 0 I guess u = X(x)T(t), and plug u_tt, u_xx into PDE and divide by u to get: T''/T = X''/X + 1 = K I solve X'' + (1-K)X = 0 first. From...

Why does the laplacian of u=0 when u is a solution to a certain boundary problem? Is this always the case?

I have formula for 1D wave equation: (*) u(x, t) = 1/2 [ f(x + ct) + f(x - ct) ] + 1 / (2c) Integral( g(s), wrt s, from x-ct to x+ct ) I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1 - x). However, for (*) to work, the initial position f(x) and initial velocity...

In the HW section, someone proposed: u^2\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0;\quad u(x,0)=x As per "Basic PDEs" by Bleecker and Csordas", treating this as: F(x,y,u,p,q)=0\quad\text{with}\quad \frac{\partial u}{\partial x}=p\quad\text{and}\quad\frac{\partial...

I am looking for an elegant way of demonstrating the parabolical behavior of the system: \frac{\partial u}{\partial x}+\frac{1}{r}\frac{\partial}{\partial r}(vr)=0 u\frac{\partial u}{\partial x}+v \frac{\partial u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r...

I got the following PDE: Laplasian[F]+a*d(F)/d(teta)=E*F I worked with cylindrical coordinates (r,teta,z) (teta is the angle between the x-axis and the r vector (in xy plane)) a,E are constants I got the constrains: z=0 r=a , so the whole problem is on a simple ring How can I make...

1/sin(phi) * d/d\phi(sin(phi) * du/d\phi) - d^2u/dt^2 = -sin 2t for 0<\phi < pi, 0<t<\inf Init. conditions: u(\phi,0) = 0 du(\phi,0)/dt = 0 for 0<\phi<pi How do I solve this problem and show if it exhibits resonance? the natural frequencies are w = w_n = sqrt(/\_n) =2...

How do you solve this type of PDE problem: \int^t_0 e^{-(t-\tau)}\frac{d^2u}{dx^2} d\tau - \frac{du}{dt} = 0 where u(x,0) = sin x Any links or info on this will be appreciated. :

need to solve the following beam equation: p(x)\frac{d^2\w}{dx^2}-a\frac{d^4\w}{dx^4}-b\frac{d^2\w}{dt^2}=0 don't have experience with pde's, thanks in advance for any hints...

The parabolic approximation was introduced by Leontovich and Fock in 1946 to describe the propagation of the electromagnetic waves in the Earth atmosphera (see Levy M. Parabolic equation methods for electromagnetic wave propagation, 2000). However, the parabolic equation was known long before...

Hello, How can i proof the existence of a solution of a PDE on H^(-1)( Omega)? :mad:

[SOLVED] Solving PDE I am just wondering, is there any gerneral method in solving PDE's or just by guess works?? thanks...

I'm working on solving coupled PDEs (mass diffusion - heat transfer - continuum mechanics) in problems where the solution domain changes depending on the solution (call it an intrinsic coupling if you will). This happens either due to addition of material to the domain or damage of the domain...

"Verify that, for any C¹ function f(x), u(x, t) = f(x - ct) is a solution of the PDE u_t + c u_x = 0, where c is a constant and u_t and u_x are partial derivatives." I managed to get the solution for this and a similar problem by showing that the new variable (x - ct in this case) satisfies...

I need your help, fellows ! I need the title and author of a good book on PDE. And also a good book with exercises on PDE. Can you help me, please ? :cry: regards Looker

du/dt = f(u)+D(laplacian*u) where u=u(x,y,t), D>0, f(u)=a*u I'm not sure where to start other than substitute f(u) with a*u. Suggestions?

Hi, I am quite new to the concept of stochastic equations. I am learning of it from some financial textbooks, however they lack a bit in the approach. Let me see if i understood Feynman-Kac: for every PDE in N dimensions (with second derivatives equivalent by unitary/orthogonal...

I have an assignment due at the end of the week, and I was wondering if someone could check my working for me, as I am prone to making errors. Also, in Step Five I am unsure how to solve for T(t), can anyone point me in the right direction? &part;u/&part;t = (c/r)*(r(&part;u/&part;r)) +...