Pdes Definition and 148 Threads

Homework Statement The question is here: http://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/assignments/probwave1solns.pdf It's a long question and I figured attaching the link here would be better. I need help with the question on page 4. when...

Homework Statement fn(x)= e-n*x Determine whether or not the sequence fn converges pointwise for each x\geq0 Homework Equations when a sequence of functions converges pointwise, the following is satisfied. f(x)=limN->inffn(x) The Attempt at a Solution I tried to graph it and I...

Hello: I am wondering if there is a general way of splitting the following PDE into two separate equations. I would like to re-write the second-order spatial derivatives on the LHS as first-order derivatives. \[ \frac{{\partial p^2 }}{{\partial x^2 }} + \frac{{\partial p^2 }}{{\partial...

Sorry about the format, bit I have no knowledge of LateX. A,B - are real constants U=(Ux,Uy,Uz) I have a system of three coupled linear second order differential equations (di)^2(Ui) +A*Laplacian(Ui)+ B*di[Divergence(U)] Note: The first term is not a sum. 0<z<H, while x & y can...

I'm reading a text on PDEs.. I'm trying to follow some of the argument the author is presenting, but I'm having a bit of difficulty. We start w/ a collection of p functions in n variables (with p <= n). That is to say, we have: u_1, u_2, ..., u_p where u_i : \mathbb{R}^n...

I should find the general solution of the two following trivial PDEs. u=u(x_1,x_2,...,x_n) 1) \frac{\partial u}{\partial x_1 \partial x_2} = 0 2) \frac{\partial u}{\partial x_1} - u = 0

Homework Statement A stretched string occupies the semi-infinite interval -\infty<x\leq0. y(x,t) := f(x-ct) + f(-x-ct) is a solution of the wave equation. What boundary condition does y satisfy at x=0? Describe what is going on in terms of incident and reflected waves. Homework...

Hi all, Suppose the solution of a pde exists and is unique, what can be said about the smoothness thereof? In general, is there some theory regarding the smoothness of the solution and its derivatives and how it depends on the boundary and boundary values? For example, if the boundary values...

I'm doing a course in PDEs, where the lecturer hasn't really explain when all these methods for solving PDEs are suitable. How do you decide which method to use to solve PDEs? Can someone explain for which class of PDEs do the following methods work: - similarity solutions - separation of...

I'm working on discretizing pde with boundary and initial conditions. The assumption of the method is that functions must be at least twice differentiable. I have an intial condition given by the following function u(x,0)=f(x)=\left\{\begin{array}{cc}x,&\mbox{ } 0 \leq x <1\\2-x, & \mbox{ } 1...

I'm taking a first course in PDEs this term (I'm a physics student) and we are using "Beginning Partial Differential Equations" by Peter V. O'Neil, which I find almost unreadable. Can anyone recommend a good book appropriate for an introductory PDE course? I have taken a standard ODE and...

According to wikipedia the greens function is defined as: L G(x,s) = - \delta(x-s)\, http://en.wikipedia.org/wiki/Green%27s_function#Definition_and_uses when L is a differential equation then the greens function is the impulse response of the differential equation. If a Hilbert space...

Hi all, A diffusion equation is of the form \frac{\partial u}{\partial t}=k \frac{\partial^2u}{\partial x^2} Usually an equation like this seems to be solved numerically using the Crank-Nicolson method: \frac{u_{i}^{n + 1} - u_{i}^{n}}{\Delta t} = \frac{k}{2 (\Delta x)^2}\left((u_{i + 1}^{n +...

DEs in general are something that I find very interesting. Though my knowledge of DEs are very rudimentary to say the least, I find them fascinating. In particular, I want to learn about PDEs and obtain a deeper understanding for ODEs. My question is, then, what kind of math preparation...

Can anyone recommend me a good book on PDEs? I'm looking for something more rigorous, for math majors, and being moderately priced is a plus too.

Does anybody know a good introductory book on PDEs? I am a physics major and something applied is what I'm looking for. It must have a good amount on Fourier methods too. Thanks.

Right now I'm a freshman physics student, interested in eventually going to grad school for theoretical physics. I may transfer and go for a mathematical physics degree at another schppl, but I can't help but wonder how much math is acutally needed past partial differential equations. Will...

Can someone explain Charpit's Method to me (PDEs) ! Thanks

Homework Statement 6 1st order, nonlinear PDEs in one space and one time variable. 6 variables are function of space and time: a, b, c, d, e f 2. The attempt at a solution Method of lines - Discretize in space. Turns system of PDEs into a much larger system of ODEs. The time term...

Is there a way that I can label contours for PDEs on Matlab? They have a few functions for drawing contours, e.g. but they're unlabelled (what's the use!) I'm sure there's a way to label my contours if I could plot them in the first place, but searches yield none. I understand that there's a...

Hi In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as (i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)] in an introduction to second order PDEs I'm a bit confused by this. Where did it come from? Can anyone explain Thanks

Hi In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as (i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)] in an introduction to second order PDEs I'm a bit confused by this. Where did it come from? Can anyone explain Thanks

Hi Does anybody know if there is an engine on the net that will solve PDEs. I'm looking for the solution of a linear first order PDE Thanks

Hello, I have been struggling at solving what I think is a system of 1st order PDEs. Here is what I have: \frac{dy1}{dt1} = y1*F1(t1,t2) + F2(t1,t2) \frac{dy2}{dt2} = y2*F1(t2,t1) + F2(t2,t1) These equations have been obtained after modeling a problem using the game theory. More...

Hi all, I have another post on here relating to Fick's law of diffusion, but before I asked that I really should have started with this question: How do you go from a one dimensional version of the diffusion equation to a cylindrical co-ordinate system of the same equation? I have found...

Hello friends, I'm reading about PDEs and my textbook lists 'integrals' of the pde f(x,y,z,p,q) = 0 where p = \partial z/\partial x and q = \partial z/\partial y, as 1. Complete Integral 2. General Integral 3. Singular Integral 4. Special Integral (solution that can't be...

There isn't one to go along with the course, and I imagine a textbook would be good to have, since this course seems like it will be quite difficult.

This problem may be very easy or very difficult (probably the first), but I can't seem to make sense of it, and that annoys me. It's not all that important (at least not yet), but I just can't seem to let it go. Anyways, here it is. Consider the following PDE: \frac{\partial^2 f}{\partial...

Laplace Transforms on Partial Differential Equations - Non-dimensionalization too! Homework Statement The experiment described in the previous problem was analyzed from the point of view of long time \left(\frac{D_{AB}\,t}{L^2}\;>>\;1\right). We wish to reconsider this analysis in order to...

What are some methods of solving parabolic PDEs apart from separation of variables and numerical methods?

Do people find solving PDEs involving characteristics, expansion waves and shocks difficult? I find it extremely difficult. It is hard to get one's head around it. Are there any ways of making it easier?

Homework Statement If you are presented with a PDE with a d(u)/dt in it, how would you classify it? There is not t dependence in the classification section of PDEs http://en.wikipedia.org/wiki/Partial_differential_equation

Is it possible to develop intuitition for solving PDEs? If so how? At the moment they seem foreign to me and I don't really see the big picture which isn't helpful and limits my problem solving skills with regards to PDEs.

I need guidance regarding PDE. If u have a nonlinear PDE as Ut+Us+a*U*Us*b*Usss=0 where U is function of (s,t) and a,b are constants. by introducing new variable x=s-t we will get Ut+a*U*Ux+b*Uxxx=0 Ut means partial derivative w.r.t time Us means partial derivative w.r.t s. How can we...

Greetings to all. In a physics problem, I have come across a system of coupled PDEs for 2 functions B(r,t) and V(r,t) on E^3 equipped with polar spherical coordinates (r,t,p). (I write t for theta and p for phi.) With a comma denoting partial derivation and D^2 denoting the Laplacian, the...

I have a system of two PDEs: y_t+(h_0v)_x=0 \quad (1a) v_t+y_x=0 \quad (1b), where h_0 is a constant. Then I want to show that (1) has traveling wave solutions of the form y(x,t)=f(x-ut) \quad (2a) v(x,t)=g(x-ut) \quad (2b), where u is the propagation velocity...

For conventional PDEs like diffusion, waves, it seems the standard way to solving them is in two steps. 1. Use separation of variables method to make them into ODEs 2. Use eigenvalues and eigenfunctions theory on ODEs to construct the final solution consisting of an infinite number of...

Hi all, I'm facing a bit of a dilemma regarding subject choices for the second semester of second year univeristy and I was wondering if anyone could lend some of their advice. First a bit of context. I'm enrolled in a BSc (Advanced) degree at The University of Sydney, Australia with a real...

Hi all, I'm facing a bit of a dilemma regarding subject choices for the second semester of second year univeristy and I was wondering if anyone could lend some of their advice. First a bit of context. I'm enrolled in a BSc (Advanced) degree at The University of Sydney, Australia with a real...

there's something about these PDE:s that I don't understand, can't find out how it really works. Here comes a problem that we can discuss. 2 equal 0.2m think iron plates got the temperatures 100 and 0 degree C from the beginning. At the time t = 0 are these 2 plates laid next to each other...

PDE + shock ! Ux + 2Uy = 0 I.C: U(x,y=2x) = exp(x) solution:- y=2x+c1 x=c2 using I.C c1=0 c2=exp(x) No solution since I.C on the characteristics line every thing is ok until here but my teacher said that there exist one case that when u change some thing u will get a...

Hi there, Does anyone know of a proof of why, in partial DEs, one can assume the existence of variable seperable solutions, then take the linear combination of all of them to be the general solution? Why can't there be any other funny solutions that fall outside the space spanned by these...

My second test in my partial differential equations class is coming up in a few days and I truly have no idea how to study for it. The first test I bombed, so I really need to do much better this time. It is the toughest math course I have encountered so far. I mean ODEs are a joke when...

Just need some verification. Question 1 Find the general solutions of the following first order PDE z_x - yz_y = z Question 2 Find the general solution of the following first order PDE x^2z_x+y^2z_y = xy

I am trying to match a result in one of my textbooks. To assist with one of their arguments they are approximating a 2nd order PDE by using a difference quotient and they show the approximation as follows: (d^2u[x,t])/(dx^2) =~ (1/h^2)(u[x+h,t]-2u[x,t]+u[x-h,t]) When I actually use...

I am looking for a method to solve coupled first order PDEs in following form: \frac {\partial u1} {\partial x} = f(x,t,u1,u2) \frac {\partial u2} {\partial t} = g(x,t,u1,u2) Subject to prober BC and IC. and consider: u1=F(x,t) u2=G(x,t) I am looking for...

Forgive me for the long post, but I'm in some desperate need of clarity on this matter. I just can't seem to grasp the whole shock wave concept, or at least the meaty part of it . I only have a couple of problems left to do to finish my HW I'm at an impasse until I dispel my confusion. I...

I have two unknown function namely u(x,y) and v(x,y). These functions are part of two coupled partial differential equations. I realize that it will be almost impossible to get a general solution seeing as one on the PDEs is non-linear. But given a set of boundary conditions I wish to solve for...