Pde Definition and 856 Threads

Homework Statement Solve ∇2T(x, y) = 0 with boundary conditions T(0, y) = T(L, y) = T0 T(x, L/2) = T(x, -L/2) = T0 + T1sin(πx/L) Homework EquationsThe Attempt at a Solution Set T(x, y) = X(x)Y(y) Then ∇2T(x,y) = (∂2X/∂x2) Y + (∂2Y/∂y2) X = 0 Rearrange to find two separate ODEs: d2X/dx2 =...

I've recently been making some posts around the web and on this forum attempting to figure out how to use a PDE that models traffic flow in concrete examples. I realize that I have to solve this PDE in order to use it, but I'm sort of lost on how exactly one solves it. The PDE is as follows...

Homework Statement Consider the wave equation: u_{tt} - c^2u_{xx} = f(x,t), \hspace{1cm} for \hspace{1cm} 0 < x < l \\ u(0,t) = 0 = u(l,t) \\ u(x,0) = g(x), u_t(x,0) = f(x) \\ Find a nontrivial solution. Homework EquationsThe Attempt at a Solution Here's what I did, but I have little...

Homework Statement Show that the set {sin(nx)} from n=1 to n=∞ is orthogonal bases for L^2(0, π). Homework EquationsThe Attempt at a Solution Proof: Let f(x)= sin(nx), consider scalar product in L^2(0, π) (ƒ_n , ƒ_m) = \int_{0}^π ƒ_n (x) ƒ_m (x) \, dx = \int_{0}^π sin(nx)sin(mx) \, dx =...

Homework Statement Solve y*∂Ψ/∂x-(x/3)∂Ψ/∂y Homework EquationsThe Attempt at a Solution My teacher told me to try separation of variables but and I tried to set Ψ=X(x)Y(y) where X is a function of just X and Y is a function of just y but when I got the solution and put it into the original pde...

Hi everyone. In electrical engineering, when you study control theory, you're taught that electrical circuits can be used to simulate the behaviour of complex systems. What I don't understand is, what are the limitation of this sistem, and why it can't be obviouslly used in a general way to...

Sorry to keep the title too broad and general. I'm starting learning pde by myself , using "linear partial differential equations for scientists and engineers" I'm having some problems with the basics "I took ODE". The following differentiation is totally new to me, can some one explain to me...

Homework Statement Consider the nonlinear (ordinary) differential equation u' = u(1-u). a) Show that u_1 (x) = e^x/(1+e^x) and u_2(x) = 1 are solutions. b) Show that u_1+u_2 is not a solution. c) For which values of c is cu_1 a solution? How about cu_2 ? Homework Equations N/a The Attempt at...

Homework Statement In my PDE course we have a homework question stating the following: Let ϑ(x) = x in the interval [-pi, pi ]. Find its Fourier Coefficients. Homework Equations From my notes on this type of question: a_o = 2c_o = 1/pi * integral from -pi to pi [f(x) dx] a_n = c_n + c_(-n)...

Hi guys, I've distilled the 3D Diffusion Equation into the following PDE using Fourier spectral techniques: ∂C(m,n,p,t)/∂t + k(p^2+m^2+n^2)C(m,n,p,t)=0, where C is the Fourier coefficient of the 3D Fourier transform, {m,n,p} are the spatial frequencies, and t is time. I've tried using a...

Homework Statement Consider the homogeneous Neumann conditions for the wave equation: U_tt = c^2*U_xx, for 0 < x < l U_x(0,t) = 0 = U_x(l, t) U(x,0) = f(x), U_t(x,0) = g(x) Using the separation of variables, find a nontrivial solution of (1). Homework Equations Separation of variables The...

This is maybe more a maths question. In part 3 of his 1905 SR paper, how does Einstein solves the following PDE : to get : ?

Question: For a vector field (ux, uy, uz), I wonder if anybody knows if there is a formal name or another mathematical expression for statement below? (∂ux/∂x)^2+(∂uy/∂y)^2+(∂uz/∂z)^2+2(∂ux/∂y)(∂uy/∂x)+2(∂uy/∂z)(∂uz/∂y)+2(∂uz/∂x)(∂ux/∂z) It is obvious that each of partial derivatives used in...

So It is well known that the 2D solution to the Laplace equation can be obtained by changing to complex coordinates ##u=x+iy## and ##v=x-iy##. This can be extended to n dimensions as long as the complex coordinates chosen also solve the Laplace equation. For example in 3D...

Tomorrow I embark on a new semester and this semester I have the pleasure of learning applied partial differential equations and the software of "ROOT" ROOT: https://root.cern.ch/ So I am here to solicite advice. 1. In regards to ROOT, is there anything that can set me up better for a more...

Homework Statement Wave equation: ytt=yxx Initial conditions: Y(x,0) =f(x) = x (0 ≤ x < 1) 2.5(5-x) (1 ≤ x < 3) 0 (Otherwise) and yt(x,0) = 0 Boundary condition: y(0,t) =0 Semi infinite domain: 0 ≤ x < infinity Homework Equations d'Alembert solution...

We have this Equation as bioheat equation: ∂T/∂t = α ∇2T + 1/ρc[S+Sp+Sm] and also this: Sp=mbcb(Tab-T) that all α,ρ,c,S,Sm,mb,cb,Tab are constants, now I want to solve this equation in conditions below with pdepe in MATLAB: There is a Tumor as a sphere with radius 1 cm exactly in center of a...

Hi everyone. I was just reading Evans' book on PDE, and, at some point, it asked to prove that an holder space is a Banach space, and I tried to do that. I just want to ask you if my proof is correct (if you see dumb errors, just notice also that I study EE, so I'm not much into doing proofs...

Hi, I use the software COMSOL Multiphysics. I would like to get the solution outputs of the mathematical problem that I run. Specificaly I would like to get pressure and velocity (according to time) of the flow that is flowing through a mean. Do I have this ability in comsol multyphysics? How...

Firstly, my main question boils down to speaking about the initial conditions and boundary conditions. I was given: $$ u(0,y,t) = u(\pi,y,t) = u(x,0,t) = u(x,\pi,t) = 0 $$ but then the initial condition was: $$ u(x,y,0) = 1 $$ Aren't the initial and boundary conditions inconsistent in such...

Homework Statement Consider the following pde: ##\sum_{i=1}^n c_i f_{x_i} = 0##, where all the ##c_i## are real valued and ##c_1 \neq 0##, and ##f## is the unknown defined from ##\mathbb{R}^n\to \mathbb{R}## and of class ##{\cal C}^1(\mathbb{R}^n,\mathbb{R})## Show there exists an invertible...

Homework Statement Find all ##{\cal C}^1(\mathbb{R}_+^\star \times \mathbb{R},\mathbb{R}) ## solutions to the pde ##x\frac{\partial f}{\partial y} - y \frac{\partial f}{\partial x} = cf##, where ##c## is a constant. Use a polar change of variable. Homework Equations Trying to bring the...

Hello. I was wondering if anyone here had come across an equation similar to this one: \alpha(uu_x)_x= u_t Any info regarding this equation or tips on how to solve this would be appreciated :) I came across these solutions: http://eqworld.ipmnet.ru/en/solutions/npde/npde1201.pdf, but how do...

Greetings all, I am registering for spring 2016 courses and have one question. I can pick up a math course and I have the option between two courses: 430 Formal Logic vs. 481 Applied Partial Differential Equations. I am a math and physics double major. Course list and description...

Homework Statement The wave equation for ψ(t, x) in 3D is ##\frac{\partial ^2 \psi}{\partial t^2}## - Δ ##\psi =0## Let ϒ(x) satisfy Δϒ = λϒ where λ<0. The x is in bold presumably to indicate it is in 3D, so represents also y and z? Show there is a solution of the form ψ(t, x) = sin(ωt)ϒ(x)...

Homework Statement The wave equation for ψ=ψ(t,x,y) is given by ##\frac{\partial ^2 \phi}{\partial t^2} - \frac{\partial ^2 \phi}{\partial x^2} - \frac{\partial ^2 \phi}{\partial y^2}## Use separation of variables to separate the equation into 3 ODEs for T, X and Y. Use the separation...

Homework Statement Find the general solution of Solve yux - xuy = xyu2 Next, solve the Cauchy problem with the Cauchy data x = y = u Homework EquationsThe Attempt at a Solution My teacher told us we should investigate how to solve this. The problem is we just have seen linear first order PDE...

Homework Statement ut +ux = 0 subject to u(t,x) = x on x^2 + y^2 = 1 Is this a well-posed PDE BVP? Homework EquationsThe Attempt at a Solution This is an easy one to solve: u(t,x) = f(x-t) I let t(0) = 0 as an initial condition, and so t=s => x= ts + xo, where x(0) = xo s is the variable...

Hi, I have a problem following the solution of a linearized potential flow equation in a publication by Fung. The problem describes potential flow over an oscillating plate. A boundary layer is approximated by defining a subsonic layer over the panel and supersonic flow above the subsonic...

I want to convert this linear second order general form PDE to two equations: ##ϕ_{xx}+bϕ_{xy}+cϕ_{yy}+dϕ_x+eϕ_y+fϕ=g(x,y)## Converted equations: ##a_1 u_x+b_1 u_y+c_1 v_x+d_1 v_y=f_1## ##a_2 u_x+b_2 u_y+c_2 v_x+d_2 v_y=f_2## I want to find parametric values of ##a_1 ...f_2## How can I do...

Homework Statement [/B] I'm trying to 'solve' two coupled second order ODE's with the intent of putting them in state space. My specific problem is more complex and includes additional equations which are irrelevant. Essentially I can solve the problem if I know the solution to this. x1 and...

Homework Statement A flexible chain of length \ell hangs from one end at x=0 but oscillates horizontally. Let the x axis point downwards and the u axis point to the right. Assume that the force of gravity at each point of the chain equals to the weight of the part of the chain below the point...

y = a x² + b x + c is a parabola. But, a parabola is just a kind of conic. All conics are given by a x² + b x y + c y² + d x + e y + f = 0 The same way, the graphic y = f(x), with f(x) satisfying a d²f/dx² + b df/dx + c f = 0, is just a particular graphic of F(x,y) = 0 with F(x,y) satisfying...

During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like);Ordinary...

Hello all, Homework Statement $$x{u_{xy}} - y{u_{yy}} = 0$$ Assume $$x,y \in {\rm{Reals}}$$ Homework Equations I have been able to solve this using different methods, but my classmates and I are trying to figure out if there is a way to do this using the methods from the course's text. The...

I'm reading through one of my profs papers, or starting. Actually it's 2 of my old profs, one I had for linear and one I had for diff eq. My question is in Section 1 of this paper. "We begin with an analysis of a second order quasilinear partial dif-ferential inequality for real valued...

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...

OK so i finished my first course of Differential equations at Uni and i have some curious questions The last equations we solved were PDEs solved with Variation of parameters and having to homogenize the boundary conditions They were all Sturm-Liouville problems as they called them, we assumed...

I used the following code and got the error: Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {list, set}, but received IBC the code is: how to amend this error? Btw, the second boundary condition v_x(1,t) should be approximated by the...

Hi PF! I am trying to solve a pde in MATLAB and started by using the generic code mathwork supplies and then augmenting for my purpose. After defining the function below and run the script, i can do anything to the ##f## and nothing changes. I can literally delete the line and still I receive...

Hello, I have a problem in the search for symmetries in pde. I would use Mathematica(c), does anyone know how to set up the code to obtain generators and then symmetries? Thanks for all.

Homework Statement Hi - I'm on the last chapter of this book and am a bit stuck. I am given a very basic fortran program (code attached in the zip file) and asked to 'investigate its accuracy and stability, for various values of Δt and lattice spacings'. The program is an implementation of the...

Hi - on the last chapter of this course and was feeling much better about it all, but I now confess to being back in my normal state - confused. I am given a simple fortran program (code attached in the zip file) and asked to investigate its accuracy and stability, for various values of \Deltat...

Given an energy functional $ E=\int_{0}^{\infty} \,dr.r\left[\frac{1}{2}\left(\d{\phi}{r}\right)^2 - S.\phi\right] $ I am told that discretizing on a lattice ri=ih (h=lattice size, i is i axis) leads to : $ 2{r}_{i}{\phi}_{i} - {r}_{i+\frac{1}{2}}{\phi}_{i+1} - {r}_{i-\frac{1}{2}}{\phi}_{i-1}...

Hi, struggling to follow some text which later leads to computer algorithms for Elliptic PDEs... It reads: To derive a discrete approx. to the PDE based on the variational principle,. we 1st approx. E in terms of the values of the field at the lattice points and then vary w.r.t. them. The...

Homework Statement This is not really a school problem, it's actually something I am trying to figure out. So, we have a sphere with given radius. (Actually let's assume that all the parameters are known). The sphere has equally distributed heaters and is in the beginning at constant...

Homework Statement Homework EquationsThe Attempt at a Solution I managed to do the first part of the question. But I'm not sure how to find u(x,t) with that initial condition. The solution says; "since ##u(x,0) = \sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}## Then it follows by linearity that...

I would like to reproduce results from a much older code to test a new one. I only have the old code's results in the form of plots, not data, but I need data. The older code solves the unsteady vorticity transport equation in 2D with a constant kinematic viscosity term. I'm interested in 2-D...

Hi all, I'm a newbie at MATLAB and currently trying to model a chromatographic process, I have a PDE to be solved in the form of c*D(C_RH)/Dz = D(f)/Dz + s (see code below for what functions c, f and s are made of) I have defined constant values for each of the individual parameters...

I want to solve a Laplace PDE in a polar coordinate system with finite difference method. and the boundary conditions: Here that I found in the internet: and the analytical result is: The question is how its works? Can I give an example or itd?Thanks