Pde Definition and 857 Threads

Hello all! So, I'll be taking first-semester quantum mechanics and partial differential equations this fall, and would like to get a little bit of a head start by reading/working some problems on my own this summer. After some initial browsing, I've heard mixed-to-poor reviews concerning...

Hi The equation is: \frac{dP}{dt}-A*\frac{{d}^2P}{dx^2}-B*\frac{dC}{dt}=0 dP/dt=A*d2P/dx^2 was solved using a finite difference method. If the function C(x,t) is known, is it possible to solve the whole equation by using the finite difference solution as a supplement to the complete solution...

Hey all, I was working a little on parabolic pde, and came across this (comes up in regularity theory). Consider a Hilbert triple V\subset H\subset V^* (continuous embeddings) and a linear operator A(t) from V to V*, where t ranges in some interval [0,T]. Now let w\in H^1(0,T;V^*)\cap L^2(0,T;V)...

In my research, I'm using a modified version of the wave equation: \[ c^2 \left( {\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }}} \right) = - \tau c^2 \left( {\frac{{\partial ^3 p}}{{\partial t\partial x^2 }} + \frac{{\partial ^3 p}}{{\partial...

Could someone tell me how to enter the following PDE into convode (or some other pde engine - feel free to solve it yourself if you like!). Its LaPlace's equation U_xx + U_yy = 0 given U=0 when x=0 U=0 when x=1 U=0 when y=0 U=x when y=1 I've used Convode...

Hey Guys; I'm solving PDE's with the use of Green's function where all the boundary conditions are homogeneous. However, how do you solve ones in which we have non-homogeneous b.c's. In case it helps, the particular PDE I'm looking at is: y'' = -x^2 y(0) + y'(0) = 4, y'(1)= 2...

Homework Statement We the domain be the unit disc D: D=\left \{(x,y):x^{2}+y^{2}<1 \right \} let u(x,y) solve: -\triangle u+(u_{x}+2u_{y})u^{4}=0 on D boundary: u=0 on \partial D One solution is u=0. Is it the only solution?Homework Equations Divergence Theorem "Energy Method"The Attempt at...

Homework Statement Homework Equations After simplification, the PDE is (b^2/a^2)(d^2 v/ d x^2) + (d^2 v/ d y^2) = -1 The Attempt at a Solution Obviously, it can't be solved by separation of variables. And I also failed in similarity solution.

Homework Statement Assume we are in the open first quadrant in the (x,y) plane Say we have u(x,y) a C1 function in the closed first quadrant that satisfies the PDE: u_{y}=3u_{x} in the open first quadrant Boundary Conditions: u(0,y)=0 for t greater than or equal to 0 u(x,0)= g(x) for x...

Hi guys, I have a general problem that I'm not quite sure how to solve. Suppose you have a first order pde, like Ut=Ux together with some boundary conditions. You'd do the appropriate transformations that lead to a solution plus an arbitrary function defined implicitly. How would you know...

I am trying to plot: u(x,y)=sin(x-t u(x,y)) An implicit solution to a PDE. I have no clue how to do this; I've plotted an equation like this before.

Homework Statement Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin...

Homework Statement Heat transfer problem with 3 insulated sides and heat flux in and out on one boundary. given values: q & k Homework Equations Governing Equation: \frac{\partial^{2}{T}}{\partial{x}^{2}} + \frac{\partial^{2}{T}}{\partial{y}^{2}} = 0 Boundary Conditions: @ x =...

Homework Statement consider a solution such that: -\triangle u + b\triangledown u + cu = f in domain Ω and \delta u/\delta n=g in domain δΩ where b is a constant vector and c is a constant scalar. Show that if c is large enough compared to |b|, there is uniqueness Homework Equations Energy...

Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...

I'm not going to blame anyone except for the fact that I'm probably a slow learner. Can somebody explain some of the things I'm learning in layman terms? That way I can have some context when I'm reading about them. Right now, the things I'm reading have no meaning, so it's really hard to...

To solve the PDE: y(z_x)+x(z_y)+z=y Use Method of characteristics a=y b=x d-cz=y-z Thus dx/y=dy/b=dz/(y-z) Taking first and second term xdx=ydy x^2-y^2=A x=sqrt(y^2+A) My question is, at this stage of the calculation, must we account for a negative constant A such that...

My plan is to work thru Rudin's Real and Complex Analysis, and then functional analysis, and then move on to DEs/PDEs. Right now its looking like Arnold for DEs, and Evans for PDEs. Any other recommendations? thanks

Homework Statement (a) Solve \frac{\partial u}{\partial t}=k\frac{\partial ^{2} u}{\partial x^{2}} - Gu where -inf < x < inf and u(x,0) = f(x) (b) Does your solution suggest a simplifying transformation? Homework Equations I used the Fourier transform as: F[f(x)] = F(w) =...

Homework Statement Obtain all solutions of the equation partial ^2 u/partial x^2 - partial u/partial y = u of the form u(x,y)=(A cos alpha x + B sin alphax)f(y) where A, B and alpha are constants. Find a solution of the equation for which u=0 when x=0; u=0 when x = pi, u=x when y=1...

Hi I have this problem Reduce to normal form the following equation x2d2f/dx2-y2d2f/dy2=xy. First I guess by normal form , they mean a more standard equation, for example Laplacian. I usually know what to do when the coefficients are constants, but in this case I don't know.I think it is...

PROBLEM: Verify that the functions [x+1]e^(-t) ; e^(-2)sint ; and xt are respectively solutions of the nonhomogeneous equations Hu = -e^(-t)[x+1] ; Hu = e^(-2x)[4sint+cost] ; and Hu = x where H is the 1D heat operator H = \frac{\partial}{\partial t} -...

Homework Statement Assume ut+cux = xt, u(x,0) = f(x) for t>0. Find a formula for u(x,t) in terms of f, x, t, and c. The Attempt at a Solution I don't really follow what the professor is doing in class, and his office hours and the textbook weren't much more help, so the only thing I know...

Hello, I believe this is my first post. I would like to solve the heat equation PDE with some special (but not complicated) initial conditions, my scenario is as follows: A perfectly spherical mass of water, where the outer surface is at some particular temperature at t=0 (but not held at...

hello all, im doing a research on model called RABR which supports dark and bright solitons. as first step i need to find numeric solution for the following equation: F'' = c1*F - c2*F/sqrt(c3+F^2) where c1, c2 , c3 are const, and F is function of x, i.e: F= F(x) i try to make...

Homework Statement Hi, i have the following system of equation. In the task is that system have periodic solution and have to be used polar coordinates. Homework Equations x'=1+y-x^2-y^2 y'=1-x-x^2-y^2 The Attempt at a Solution After transfer to polar system i tried to use the method...

Homework Statement So it's been a really long time since I've done any ode/linear algebra and would like some help with this problem. Derive the general solution of the given equation by using an appropriate change of variables 2\deltau/\deltat + 3\deltau/\deltax = 0 The thing that...

Find the Finite element solution for a equation: (∂^2 u)/〖∂x〗^(2 ) +(∂^2 u)/〖∂y〗^2 +λu-c=0 using linear triangular finite elememts. In the above equation u is scalar,λ is a constant and is a body force term(constant). The boundary conditons are in terms of prescribed values of the function...

Homework Statement which solutions of du/dt+du/dx=0 is equal to xe-x2 Homework Equations The Attempt at a Solution u(x,0) = xe-x2 u(x,t)= (x-t)e(-x-t)2 what else do i need to do?

Hi I have a question regarding a PDE and change of variable. I can follow through the algebra but I have a problem deciding what route to take after I use the chain rule at a later point. I have an expression: - \frac{\partial^2 f}{\partial y^2} and would like to make the variable...

I am trying to solve numerically the following PDE: dF(x,t) / dt = some function of x and F(x,t) ONLY where 0<x<5. This equation does NOT need boundary conditions at x=0 and x=5 because each point in x evolves independently from the others (the equation doesn't contain spatial derivatives)...

d^2G/dxdy+(a-1)*dG/dx*dG/dy=0 where G is a function of x and y. Moreover, what if a is not a constant, but instead a function of x and y?

Hi, could anyone tell me what kind of technique I should use to solve the following PDE? dG/dt=(n*s-u)(s-1)dG/ds Many thanks and happy new year to everyone:)

I'm solving a nonlinear pde system in one space. It looks that the pdepe function won't work, because it only accepts coupled term in 's', not 'c' and 'f'. My equations are like: \partial u1\partial t + c(u2)*\partial u2\partial t = f1(u2)*D^2 u1Dx^2 + s1(u1,u2)...

Here's my question, friends I have to define initial and boundary condition for a transport PDE: u_t+x(1-x)u_x=0 with x and t is between [0,1], to solve this equation, what kind of numerical method and boundary condition do you recommend and why? What kind of numerical error do you...

Here's my question, friends I have to define initial and boundary condition for a transport PDE: u_t+x(1-x)u_x=0 with x and t is between [0,1], to solve this equation, what kind of numerical method and boundary condition do you recommend and why? What kind of numerical error do you...

Fick's second law in general form: \frac{\partial C}{\partial t} = D\nabla^2 C In spherical form: \frac{\partial C}{\partial t} = D\frac{1}{r^2}\frac{\partial}{\partial r}\left( r^2\frac{\partial C}{\partial r} \right) (Assume all changes in phi and theta to be zero, so we are only concerned...

Is Advanced calculus absolutely necessary in order to succeed in PDE ? The problem is that my school does not require me to take Adv Calculus since i am an applied math major , i am not even required to take a proof based course here's the link for the major (...

Homework Statement Solve the 2-D time-independent Schrödinger equation with V (x,y) = 0: Homework Equations -ћ2/2m ( ∂2Ψ(x,y)/∂x2 + ∂2Ψ(x,y)/∂y2 ) = EΨ(x,y) The Attempt at a Solution I started by getting -ћ2/2m to one side: ( ∂2Ψ(x,y)/∂x2 + ∂2Ψ(x,y)/∂y2...

Homework Statement \frac{\partial^{2}u}{\partial t^{2}} = a^{2} \frac{\partial^{2}u}{\partial x^{2}} (x>0, t>0) with u(0,t) = t, u(x,0) = 0, ut(x,0) = A. Solve the PDE using laplace transform. The Attempt at a Solution I have managed to get the transform: \frac{\partial^{2}U(x,s)}{\partial...

the book gives u_{xx} - u_{tt} - au_{t} - bu = 0; 0<x<L, t>0 says if you multiply it by 2u_{t} you can get \left( 2u_{t}u_{x}\right)_{x} - \left( u^{2}_{x} + u^{2}_{t} + bu^{2}\right)_{t} -2au^{2}_{t} = 0 or \frac{\partial}{\partial x} \left( 2 \frac{\partial...

The problem: Find the value of dz/dx at the point (1,1,1) if the equation xy+z3x-2yz=0 defines z as a function of the two independent variables x and y and the partial derivative exists. I don't know how to approach the z3x part. I thought you would use the product rule and get 3(dz/dx)2x +...

I wish to find exact solutions of Laplace's equation in cylindrical coordinates on (a subset of) the 3-sphere. This pde is linear but not separable. The potential {\Phi}(x,z) must fulfil the following pde: (1-{\frac{x^2}{a^2}}){\frac{{\partial}^2}{{\partial}x^2}}{\Phi}(x,z)+...

First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem. Let L be a linear transformation defined by L[p]=(x^2+2)p"+ (x-1)p' -4p I have not seen linear transformations in this format. Usually I see something like L(x)=x1b1+ x2b2...

http://mathbin.net/906 cant figure this one out

That's right, I said dependent. Does anyone have any experience dealing with such beasts. I haven't been able to find a single mention of them in any textbook on PDEs. The thing I'm really curious to know is whether the method of separation of variables works as usual, e.g. if the dep vars...

isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body. the equation boils down to \left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial...

So I suppose my Fourier knowledge is a little bit rusty. Any help would be greatly appreciated. http://pmgz.net/3259.jpg How do they get from the original DKS equation to the Fourier space DKS equation (from eq 1 to eq 2)? Thanks greatly for any help.

Basic background info (which may not be useful):I will be a junior in physics this fall. I am done with all undergraduate level classical mechanics, E&M and quantum mechanics courses. I think I want to do experimental physics. I have been working under an AMO physics professor whose research is...

Homework Statement Consider an electrical cable running along the x-axis which is not well insulated from ground, so that leakage occurs along its entire length. Let V(x,t) and I(x,t) denote the voltage and current at point x in the wire at time t. These functions are related to each other...