Pde Definition and 856 Threads

Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...

Hi, After considerable simplification in a problem I'm working on, I end up with the following partial differential equation: \partial_{\eta}\left(\frac{\sinh\eta}{\Delta}\partial_{\eta}g\right) + \partial_{\theta}\left(\frac{\sinh\eta}{\Delta}\partial_{\theta}g\right) + c^2\left[\frac{E_{p}...

Hi, I hope I posted in the right group. I read some papers about infinite dimensional systems and gave PDEs as examples of infinite dimensional systems. So far, I still cannot get why is that so. Could everybody here help me giving relation between a PDE and an infinite dimensional...

Homework Statement Solve the IVP for the wave equation: Utt-Uxx=0 for t>0 U=0 for t=0 Ut=[dirac(x+1)-dirac(x-1)] for t=0 2. The attempt at a solution By D' Almbert's solution: 1/2 integral [dirac(x+1)-dirac(x-1)] dx from (x-t) to (x+t) I apologize for not using Latex- my...

Homework Statement Show the two problems (i.e. give the boundary conditions and PDE's) that the given problem must be broken into in order to solve the PDE uxx+uyy=2u+f(x,y) satisfying the shown boundary conditions. Homework Equations See attachment. The Attempt at a Solution We...

Homework Statement As part of the solution to a HW problem of mine, I have to solve the PDE p_t = -vk^2 p - k \delta p_k, where p = p(k,t) and v,\delta are known constants. Homework Equations I tried to look for a solution of the form p(k,t) = K(k)T(t) and found one, but I'm not sure if I...

Hello physics enthusiasts! I was looking for resources, and stumbled upon these awesome forums. I am looking for how to solve the helmholtz equation / wave equation on a figure 8 type shape. I wanted to find the resonant frequencies of a classical guitar. Would this work? I am considering...

Just learned that diffusion equation loses information as time goes on,i.e. given the initial condition at t=0, we can't uniquely determine the solution for t<0. And diffusion equation reminds me of Schrodinger equation, which looks very much like diffusion equation, except that the coefficient...

Hi, I have a system of coupled PDE's as follows: A1 * (f,xx + f,yy) + B1 * (g,xx + g,yy) + C1 * f + D1 * g = 0 ; A2 * (f,xx + f,yy) + B2 * (g,xx + g,yy) + C2 * f + D2 * g = 0 ; where, f = f(x,y) and g = g(x,y) and ,xx = second partial derivative of the function wrt x and ,yy =...

Homework Statement Solve the boundary value problem (1)-(3) with a=b=1, c=1/Π f(x)=sin(3 \pi x) sin(\pi y),g(x)=0 (1)\frac{\partial^{2}u}{\partial t^{2}}=c^{2}\left(\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}\right) 0 < x < a, 0< y <b, t > 0 (2)...

To solve a PDE, we can use the technique of separation of variables. However, this is not the most general solution. But, the mathematical trick is that we can solve for the SoV solutions and then make a general solution by adding SoV solutions together. I don't understand what this means?

I have a PDE test next week and I'm kinda confused. How do you prove that eigenvalues are all positive? I know Rayleigh Quotient shows the eigenvalues are greater than or equal to zero, but can someone explain the next step. Thanks in advance

A work problem, but more like a homework problem... Homework Statement Euler-Bernoulli beam with a lumped mass at x=L, simply supported at x=0 and x=L/2. The beam has a linear initial velocity profile v(x) = w*x. Homework Equations BCs Y(0)=0 y''(0)=0 Y(L/2)=0...

Advice on a "great" self study book. PDE Hello, for the first time this summer i won't be taking ( at least i hope so) any classes. That will give me a lot of free time to do as i please. i will be a senior in college and i still have to take pde's. The prof that teaches the course, at least...

Dear All, I have a PDE like: A * d2w/dy2 + B * 1/x * d2w/dx2 + C * w = 0 where , w = w(x,y), A & B & C are constants. Is there any analytical solution for this PDE? If not, is finite difference is the right numerical tools to solve it? Thanks, Frank

Could someone tell me where to start? I tried separating variables, which got me no where (plus we haven`t technically learned it), and I tried putting it into a form of D^2U, but I couldn`t figure that out either. Please help. Thank you.

Homework Statement a) Transform the differential equation \frac{\partial^2 f}{\partial x^2} - y^2 \frac{\partial^2 f}{\partial y^2} - y \frac{\partial f}{\partial y}=4y^4,\, with the substitution u=ye^x and v=ye^{-x} in the region y>0. b) Determine all solutions of class C^2 (that is...

Homework Statement Solve the boundary value problem for a string of unit length, subject to the given conditions. f(x)=0.05sin \pi x, g(x)=0, c=\frac{1}{\pi} Homework Equations Model: u(x,t)=X(x)T(t) Which yields two separated equations by the one dimensional wave equation. X''-kX=0 and...

I am trying to solve this partial differential equation \frac{\partial^2 \rho (x)}{\partial x^2} + (ax+b)\frac{\partial \rho (x)}{\partial x} + c \rho (x) = const a, b and c are constant value. Could someone give me a general solution of this king of ode? Thanks in advance.

Homework Statement The equation is ut + uux + uxxx = 0 I need to show that this is a parabolic pde. Homework Equations Hint : convert to an equivalent system of 1st order equations by introducing an auxiliary variable p = ux, etc. The Attempt at a Solution So i took p = ux doesn't that...

Homework Statement Attached image please, sorry I tried LaTeXing and i failed super hard. Homework Equations Fundamental Theorem of Calculus Multivariate chain ruleThe Attempt at a Solution I'm basically at a loss of words on this question. I might be thinking of this incorrectly but what my...

Homework Statement Hey I'm trying to get a sense of this problem, just starting pde class: au_x+bu_y+cu=0 Homework Equations The Attempt at a Solution Dunno what to do with that last term

Homework Statement Simplify the expression e^(i6theta)[ (1+e^(-i10theta))/(1+e^i2theta)] Answer should be in terms of cosines but i don't know how to start this problem? :S Also, does e^(-iwt) = - coswt -jsinwt? K so I am thinking about Eulers formula, and I get an expression with Sines...

I am attempting to solve the following PDE using the GUI for Matlab's PDE toolbox. \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } \pd{\Psi}{y}{} + \pd{\Psi}{x}{2} + \pd{\Psi}{y}{2}=0 Is this possible? I have been able to use the PDE toolbox for...

HI, I have solved the diffusion equation using the central difference scheme. Next, I would like to code this diffusion equation with a nonlinear term added to the equation. The full equation is as follows: dS/dt = Ds * d^2S/dx^2 - aS/b+S Since aS/b+S is a nonlinear term, I need to...

Dear All, I am trying to solve the following system of PDEs \frac{\partial{A}}{\partial{t}}= a_{2}\frac{\partial{{^{2}}A}}{\partial{x^{2}}}-a_{1}\frac{\partial{A}}{\partial{x}}-a_{0}A+b_{0}B \frac{\partial{B}}{\partial{t}}=...

Hi, well let me put the question a bit clear...my concern area is on ode and pde...my question is when you solve a pde/ode analytically and get a solution by asymptotic means does this mean that if solution exists then ...when using convergence as an alternative way of getting solution of the...

Homework Statement I am not even sure if the title is correct - it's day two of the class and I am already lost beyond belief. Anyway...here is the question. Consider the equation (1) \frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} = 0 Where u=u(x,t) is the unknown...

If a PDE has no boundary conditions specified, how does one go about providing a solution--even if this is a general solution? I'm stuck looking at the separation of variables and other methods which all seem to heavily rely on those boundary conditions and initial conditions. If anyone...

How does this compare to other undergraduate intro PDEs texts? http://www.math.umn.edu/~olver/pdn.html

I've tried and failed to search for this on the forum, so apologies if this has been answered many times before. Given a variable u which is a function of x and y: u = u\left(x,y\right)\\ is it possible to solve the pde: Au_{xx} + 2Bu_{xy} + Cu_{yy} = D\\ The knowns are: The real...

Homework Statement Find the distribution of temperatures in the rod of length L with the follow BC and NC Homework Equations u_{t}=\alpha u_{xx}\,\,\,x\in]\frac{-L}{2},\frac{L}{2} u(\frac{-L}{2},t)=u(\frac{L}{2},t)=700 u(x,0)=300\,\,\,x\in]\frac{-L}{2},\frac{L}{2} The Attempt at...

Hi! Merry christmas! Homework Statement u_{t}=u_{xx}-u_{x} Can I solve it with separation of variables? The Attempt at a Solution u=XT XT^{'}=T(X^{''}-X^{'}) After rearranging \frac{T^{'}}{T}=-\lambda^{2} 1) \frac{X^{''}}{X} - frac{X^{'}}{X}=-\lambda^{2} The solution to 1) is...

Solving a PDE with Polar coordinates yu_x-xu_y=0 x=r\cos{\theta} \ \mbox{and} \ y=r\sin{\theta} u(r,\theta) Does u_x\Rightarrow u_r \ \mbox{or} \ u_{\theta} \ \mbox{and why?} Thanks.

I am using the book Elementary Partial Differential Equations by Berg and McGregor. However, the book neglected to discuss problems of the this form, uu_{xy}-u_xu_y=0. How do I approach this problem? Thanks.

Dear Friends, I encountered with some difficulties in solving following PDE (off course, analytically not numerically), so I would really appreciate it if you help me in this matter. The PDE is: Uzz+f(t)*Uz=g(t)*Ut where U(z,t), f(t), and g(t) B.Cs and I.C are: U(0,t)=b...

Hi, I have a couple of questions remaining on a differential equations example sheet that I can't seem to crack. They have a common theme -- changing variables in a PDE. Here's the first one. I'm hoping that with a gentle nudge in the right direction the rest of it should fall into place...

Homework Statement Show that the mass is a constant of the motion (invariant) for the KdV equation by direct differentiation with respect to time.Homework Equations KdV equation: u_{t}+u_{xxx}+6uu_{x}=0 mass: \int udx (integral is taken over whole line) The Attempt at a Solution \frac{d}{dt}...

Hi, I need some help, looking at a PDE of the form: F'(x) * F(x) + Cte * F(x) = g(x) Cte is a constant independent of x with of the simple form : g(x) = Constant* (1/x ) Please excuse my ignorance, but does this equation have an analytical solution or do i need to resort to...

Homework Statement Question: Show that the solutions of the wave equation for a square drum head of side L can be written as: u(x,y,t)=\sum_{k_x , k_y} A_{k_x , k_y} e^{-ik_x x - ik_y y}e^{i\omega t} where: \omega = a \sqrt{{k_x}^2 + {k_y}^2} Where a is the wave-velocity and...

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

Homework Statement Let D be a region in R^2 . Let's denote: K= \{ (x-a)^2 + (y-b)^2 + c | a,b,c \in R \} . 1. Prove that there is no non-trivial first order PDE F(x,y,z,z_x ,z_y)=0 such as its set of soloution in D includes all the functions in K. 2. Find two non trivial differential...

Homework Statement I am trying to derive the partial differential equation for the change in the ratio (r) of two solute (C1, C2) with time during 1D flow of a reacting advecting-diffusing fluid moving through a porus media. I can define the partial differential equations for the individual...

I need help with this PDE, it's not an homework, I need to solve it for my thesis and it has physical application...anyway the problem is: \frac{dx}{dt}=f(t)g(r)+\frac{v}{r}\frac{d (Rx)}{dR} f(t) and g(r) are known. I can solve the equation with only the first or the second term ...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

Homework Statement Solve u_{tt} - 4u_{xx} = 0, x \in \mathbb{R}, t > 0 u(x, 0) = e^{-x^2} , x \in \mathbb{R} Homework Equations General solution to the diffusion equation: u(x, t) = \frac{1}{\sqrt{4\pi kt}} \int\limits_{-\infty}^{\infty} e^\frac{{-(x - y)^2}}{4kt} \varphi(y) \, dyThe...

Homework Statement Uxx + 3*Uyy - 2*Ux + 24*Uy +5*U = 0 Reduce this to the form Vxx + Vyy + C*V = 0 U = V*e^(alpha*x + Beta*y) y' = gamma*y Ok, the problem I am having is I don't know what to do with the gamma, however I am off by a factor of 3 in my answer for Vyy, so I know gamma...

The "Bender and Orszag" analog for PDE There is a famous book written by Bender and Orszag named "Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory" which explains how to obtain approximated solutions for ordinary differential equation. Well...

Hi, I've spent days trying to solve some equations in a paper (referenced below) that describes it as a "straightforward, albeit lengthy integration," but I can't work out the "straightforward" bit. The notation is also odd, which doesn't seem to help my problem. Perhaps someone could help...