Pde Definition and 743 Threads

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

Advice on a "great" self study book. PDE [FONT="Arial Black"]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...

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 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 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 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...

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...

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...

I'm trying to solve equation in the attached pdf, which describes anistropic diffusion in 3D with an additional term to account for hydrogen bonding and unbonding of the diffusing substance to the medium. I've considered Laplace transforms, then solving in the Laplace domain, then inverting...

Im a rising junior in the US starting my upper division physics classes. I have an opening this quarter and want to take an applied math course, but cannot decide between these two: In the mathematics department: "Applied complex anlysis Introduction to complex functions and their applications...

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...

find the general solution of yux+xuy=yu+xex ( the solution is in the form of u(x,y)=yex+f(y2-x2)ex ) if at first the value of u(x,y) on the upper half of hyperbola (that is y>=1) has been given as φ,show that if φ has not been given as a special form there is no solution.find that special form...

Hello all! I appreciate it if you can share any thoughts that you may have regarding how to solve the following PDE: \frac{\partial U(z,t)}{\partial t}+(1-z)\frac{\partial U(z,t)}{\partial z}=(\frac{1}{z}-1)\left(U(z,t)-U(0,t)\right) Initial condition:U(z,0)=z^{K} U(0,t) arises due...

Why is the characteristic of (d/dx) + (d/dt) = 0 where d is small delta c = x - t and not c = x + t

I have the following equation to solve: u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx} I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do...

Homework Statement I have the damped wave equation; u_{tt} = 4 u_{xx} -2 u_{t} which is to be solved on region 0 < x < 2 with boundary conditions; u(0,t) = 2, u(2,t) = 1. i must; 1) find steady state solution u_{steady}(x) and apply boundary conditions. 2) find \theta(x,t)...

Homework Statement Question attached Homework Equations The Attempt at a Solution I'm mostly wondering with c) and also want to check if my solution is correct. My solutions for this question are: u(x,t)= -1/2 for x <= -1/2*t = 1 for -t < x < 1-t = 1/2 for x =>...

Hi. I'm following the solution of a Klein-Gordon PDE in a textbook. The equation is \begin{align} k_{xx}(x,y) - k_{yy}(x,y) &= \lambda k(x,y) \\ k(x,0) &= 0 \\ k(x,x) &= - \frac{\lambda}{2} x \end{align} The book uses a change of variables $\xi = x+y$, $\eta = x-y$ to write \begin{align}...

I need to solve the following system of differential equations: \frac{\partial^2 y}{\partial t^2} + A\frac{\partial y}{\partial t} - B \frac{\partial^2 y}{\partial z^2} = Cq \frac{\partial^2 q}{\partial t^2} + D\frac{\partial q}{\partial t} + q = E\frac{\partial^2 y}{\partial t^2}...

I'm trying to solve this equation: Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0 I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...

[SIZE="5"]I need to know some of the application of partial differential equation in mechanic ? just need some headlines and I 'll Google them . thanks

Hi, I have this problem, I need to plot the solution of the next nonlinear-PDE problem: y_{tt}=((y_x)^3)_x+y^3-y where y=y(x,t), and we are looking for a solution with a compact support in (-x0,x0) (which I need to find x0), i.e the solution vanishes for x>=x0 or x<=-x0, and also y=y_x=0 on...

From PDE to ODE ?! + research Homework Statement In the attached research, What are the steps that we work to transform the equation (1) to (8) Homework Equations (1) and (8) The Attempt at a Solution I know that they used similarity transformations but I do not know how to do...

I am a senior in mathematics studying graduate point-set topoology atm. I am thinking I want to study differential topology in graduate school and maybe apply it to problems in cosmology. Do I need to take more ODE and PDE? I took intro to diff eq- the one that all engineering undergrads take...

Hey guys, I'm having a little difficulty with a pde I'm trying to solve. It boils down to solving for a first integral. I don't want the answer, but I'd be glad to get a little help. We have the system: \frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{xy(z^2 + 1)} We can use the first two and find...

Dear all, I'm trying to solve the diffusion PDE for my system, shown below: \frac{\partial C}{\partial t} = D (\frac{\partial^2 C}{\partial r^2} + \frac{1}{r} \frac{\partial C}{\partial r}) where C is the concentration, changing with time t and radius r. D is the diffusion...