Read about pde | 67 Discussions | Page 1

  1. DuckAmuck

    A Separation of variables possible in this problem?

    Is it possible to use separation of variables on this equation? au_{xx} + bu_{yy} + c u_{xy} = u + k Where u is a function of x and y, abck are constant. I tried the u(x,y) = X(x)Y(y) type of separation but I think something more clever is needed. Thank you.
  2. G

    Method of characteristics: Discontinuous source

    Hello all, this question really has me and some friends stomped so advice would be appreciated. Ok so, the relevant (dimensionless) continuity equation I have found to be $$\frac{\partial\rho}{\partial t} + (1-2\rho)\frac{\partial \rho}{\partial x} = \begin{cases} \beta, \hspace{3mm} x < 0 \\...
  3. Vick

    I Alternating Direction Implicit method for solving 2D Heat diffusion

    I'm trying to compute a 2D Heat diffusion parabolic PDE: $$ \frac{\partial u}{\partial t} = \alpha \{ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \} $$ by the ADI method. I am actually trying to go over the example in this youtube video. The video is in another...
  4. F

    Deriving the Adjoint / Tangent Linear Model for Nonlinear PDE

    I am trying to derive the adjoint / tangent linear model matrix for this partial differential equation, but cannot follow the book's steps as I do not know the math. This technique will be used to solve another homework question. Rather than posting the homework question, I would like to...
  5. JD_PM

    Understanding how to apply the method of images to the wave equation

    Exercise statement Find the general solution for the wave equation ftt=v2fzzftt=v2fzz in the straight open magnetic field tube. Assume that the bottom boundary condition is fixed: there is no perturbation of the magnetic field at or below the photosphere. Solve means deriving the d’Alembert...
  6. T

    A Solving scalar field propagation in a curved spacetime numerically

    Hey everybody, Background: I'm currently working on a toy model for my master thesis, the massless Klein-Gordon equation in a rotating static Kerr-Schild metric. The partial differential equations are (see, equation 27, with V'=0): $$ \partial_t\phi =...
  7. akin-iii

    I How do I derive a PDE for the volume flow rate of a tilting vessel?

    So the other day, I was pouring beer from a can to a mug and I obviously know the flow rate depends on the height of the beer from the bottom of the can (fluid level in the vessel), angle of tilt and I think time as well. I was wondering how to best model the PDE to describe such a phenomenon (...
  8. S

    Mathematica Solving 2-D partial integro-differential equation

    While reproducing a research paper, I came across the following equation, ∂f/∂t−(H(f)(∂f/∂x)=0 where [H(f)] is hilbert transform of 'f.' and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is...
  9. Safder Aree

    How to apply the Fourier transform to this problem?

    I am struggling to figure out how to approach this problem. I've only solved a homogenous heat equation $$u_t = u_{xx}$$ using a fourier transform, where I can take the fourier transform of both sides then solve the general solution in fourier terms then inverse transform. However, since this...
  10. K

    Solving a PDE with boundary problem

    Homework Statement I want to find the solution to the following problem: $$\begin{cases} \nabla^2 B=c^2 B &\text{ on the half plane } x>0 \\ B=B_0 \hat{z} & \text{ for } x<0 \end{cases}$$ in the ##xz## plane. ##c, B_0 \in \mathbb{R}## Homework Equations I am not really sure what would be...
  11. J

    I Solution for 1st order, homogenous PDE

    ##u_t + t \cdot u_x = 0## The equation can be written as ##<1, t, 0> \cdot <d_t, d_x, -1>## where the second vector represents the perpendicular vector to the surface and since the dot product is zero, the first vector must necessarily represent the tangent to the surface. We parameterize this...
  12. N

    Partial Differential Equation with variable coefficients

    Homework Statement This question relates to a very large project I have been assigned in a course on mathematical methods in structural engineering. I have to solve the following equation, in a specific way: (17) Now we have to assume the following solution: (18) It wants me insert...
  13. Auto-Didact

    A PDE: Between Physics and Mathematics

    This is perhaps the single most important mathematical physics papers I have ever read; I think everyone - especially (theoretical) physicists - interested in theoretical physics should read it. In fact, read it now before reading the rest of the thread: Klainerman 2010, PDE as a Unified Subject...
  14. C

    Solving a 2D PDE using the Fourier Transform

    Homework Statement Solve the following partial differential equation , using Fourier Transform: Given the following: And a initial condition: Homework Equations The Attempt at a Solution First , i associate spectral variables to the x and t variables: ## k ## is the spectral variable...
  15. Jozefina Gramatikova

    Separate the following PDE as much as possible

    Homework Statement [/B] Homework Equations [/B] The Attempt at a Solution [/B] Could you tell me is there something specific that I need to the with sin(xy)? Thanks
  16. M

    I How can you know if a numerical solution is correct?

    Hi PF, Suppose I numerically solve a nonlinear system of differential equations. How can I know if my solution is correct (if there is no known analytic solution)? What are the standard practices people do? I have a couple of ideas, but I want to know what people are already doing. Danke!
  17. F

    I Solving PDE's with chebychev FFT

    I have seen one lecturer solve a PDE with just using Fast Fourier Transform (##FFT##) of a function ##v## on a chebychev grid. ##v_t=\mu v_x## This lecturer uses ##FFT## on ##V##, then solves the ODE using an ODE solver in Matlab, then inverse ##FFT## to get the real solution ...
  18. Mzzed

    I Boundary Conditions for System of PDEs

    I am unsure how to choose the boundary conditions for a system of PDEs or for a single PDE for that matter. The situation I am stuck with involves a system of 4 PDEs describing plasma in a cylinder. The dependent variables being used are Vr, Vt, Vz, ni, and the independent variables are Rr...
  19. Dor

    A Numerical solution for a two dimensional 3rd order nonlinear diff. eq.

    I'm a bit lost in all the numerous methods for solving differential equations and I would be very grateful if someone could point me to some direction. I want to solve the following boundary conditioned differential equation: $$a_1+a_2\nabla f(x,y)+a_3\nabla f(x,y)\cdot \nabla^2...
  20. A

    I Classification of First Order Linear Partial Differential Eq

    How can I classify a given first order partial differential equations? Are all first order linear PDEs hyperbolic? Quora Link:
  21. A

    A Understanding dummy variable in solution of 1D heat equation

    The solution of 1D diffusion equation on a half line (semi infinite) can be found with the help of Fourier Cosine Transform. Equation 3 is the attached figure is the solution of 1D diffusion equation (eq:1). I want to write a code for this equation in MATLAB/Python but I don't understand what...
  22. P

    Periodic BC's of heat equation

    Homework Statement I have the heat equation $$u_t=u_{xx}$$ $$u(0,t)=0$$ $$u(1,t) = \cos(\omega t)$$ $$u(x,0)=f(x)$$ Find the stable state solution. The Attempt at a Solution I used a transformation to complex to solve this problem, and then I can just take the real part to the complex...
  23. P

    Solving a wave equation with seperation of variables.

    Homework Statement I am trying to solve the given wave equation using separation of variables, u_{tt} - 4u_{xx} = 4 for 0 < x < 2 and t > 0 (BC) u(0,t) = 0 , u(2,t) = -2, for t>0 (IC) u(x,0)=x-x^2 , u_t(x,0)=0 for 0\leq x \leq2 Homework Equations We are told we will need to use...
  24. i_hate_math

    Heat Kernel at t=0

    Homework Statement Show that k(x,0)=δ(x). Where k(x,t) is the heat kernel and δ(x) is the Dirac Delta at x=0. Homework Equations k(x,t) = (1/Sqrt[4*π*D*t])*Exp[-x^2/(4*D*t)] The Attempt at a Solution I am just clueless from the beginning. I am guessing this is got to do with convolution...
  25. S

    A Transforming a PDE with Laplace method

    Hello, I have the following PDE equation: a*b/U(u)*V(v) = 0 where a and b are arbitrary constants, and U an V are two unknown functions. To me it appears this has no solution, however I would like to ask if anyone has some suggestions, such as transforming it to another type using Fourier or...
  26. A

    Solving partial differential equation with Laplace

    Homework Statement am trying to solve this PDE (as in the attached picture) also my attempt is included, but i stopped in step, can you help me with it? appreciated, Homework Equations The Attempt at a Solution my attempt is the same as in the attached...
  27. R

    A Solution of a weakly formulated pde involving p-Laplacian

    Let $$f:\Omega\to\mathbb{R}$$, where $$\Omega\subset\mathbb{R}^d$$, and $$\Omega$$ is convex and bounded. Let $$\{x_i\}_{i=1,2,..N}$$ be a set of points in the interior of $$\Omega$$. $$d_i\in\mathbb{R}$,$i = 1,2,..N$$ I want to solve this weakly formulated pde: $$ 0=\frac{A}{N^{d+1}} \sum_i...
  28. FranciscoSili

    I Simple PDE

    Hello everybody. I'm about to take a final exam and i've just encountered with this exercise. I know it's simple, but i tried solving it by Separation of variables, but i couldn't reach the result Mathematica gave me. This is the equation: ∂u/∂x = ∂u/∂t Plus i have a condition...
  29. V

    I Classification of differential equation

    Hi, I have an equation that takes the form: ax''-by' + c = 0 where x'' is second order with respect to time and y' is first order with respect to time. Would this be classed as a partial differential equation? Thanks very much for your help :)
  30. A

    A Buckling PDE

    Hi I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, in mathematica with no success. I dont need it in mathematica I just need any way poosible, even matlab, or any other numeric way/soltuion. Can some one help, or even give me the final...