What is Pde: Definition and 854 Discussions

PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem.
PDE surfaces were first introduced into the area of geometric modelling and computer graphics by two British mathematicians, Malcolm Bloor and Michael Wilson.

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  1. A

    PDE as a corequisite for Quantum mechanics A

    Hi, I'll be taking Quantum Mechanics A, Electromagnetic Theory I and PDE next semester. However, in the course description, PDE is a corequisite for QM and Electromagnetic. I wanted to know what PDE topic should I read up on during the holiday that i might encounter in QM or EM before the...
  2. R

    Diffusion - Epidemiology PDE Model

    Homework Statement I'm wondering if there is an explicit traveling wave solution to a simple epidemiology diffusion model. This model is a basic representation of rabies spread among organisms. Rabies causes its victims to become delirious; hence the diffusion there. Here x is the...
  3. C

    Programs Is a Physics Major Without PDE Requirements Normal?

    well I just got into UMASS at amhearst from my community college, I should be going there in the spring but as I looked over the requirements for their physics mjor I noticed something. for the professional track they only require multivariable calculus and ordinary differential equations...
  4. M

    Photodetection Efficiency (pde)

    what is pde ? in terms of the formula , and in general so i can picture it in my mind so to speak.
  5. H

    Finding the Steady Solution for a PDE Problem

    I'm wondering if anyone can just run through how this is done. I have the solution so that's now the problem. I just need someone to provide me with the method of finding the steady solution (I can find the transient no problem). A slender homogeneous conducting bar of uniform cross section...
  6. quasar987

    Taking PDE or abstract algebra

    In my uni I am forced to make a painful choice btw taking PDE or abstract algebra. I will take algebra, but I'd like to know what I will be missing? What is being taught in this class exactly? (BESIDES HOW TO SOLVE A PDE BY SEPARATION OF VARIABLES :rolleyes:)
  7. K

    A PDE and Linear operator questions.

    Let be L and G 2 linear operators so they have the same set of Eigenvalues, then: L[y]=-\lambda _{n} y and G[y]=-\lambda _{n} y then i believe that either L=G or L and G are related by some linear transform or whatever, in the same case it happens with Matrices having the same...
  8. J

    Where to Find Solved PDE Problems Online?

    Hi, I am currently taking a class which is now covering PDE's and I think I need more sample or example problems that are already solved, particularly on Fourier series solution, d'Alembert method, etc. The book I'm using is Kreyszig, Advanced Engineering Mathematics, 9th edition. Are...
  9. D

    Can the PDE u_{xx}-3u_{xt}-4u_{tt}=0 be solved with given initial conditions?

    Solve u_{xx}-3u_{xt}-4u_{tt}=0 with initial conditions u(x,0)=x^2, u_t(x,0)=e^x. I got that u is an arbitrary function F(x+t), which makes no sense. I factored the operator into (\partial/\partial x+\partial/\partial t)(\partial/\partial x-4\partial/\partial t)u=0, but I can't get anywhere.
  10. P

    Eigenfunction expansion method in PDE solutions

    How does this method work? What are the mathematical ideas behind this method? Unlike separation of variables techniques, where things can be worked out from first principles, this method of solving ODE seems to find the right formulas and apply which I feel uncomfortable about.
  11. S

    Stumped? Need Help with PDE Problem - Sarah Needs a Hand!

    hmmm i have no idea where to even start with this problem, i cannot find any examples that are similar or anything like that anywhere! http://img147.imageshack.us/img147/2319/picture18ur9.png anyone got an idea as to a good first step to take? thanks sarah :) edit: i tryed something wild...
  12. S

    PDE problem : diffusion equation help

    Hi all, I am stuggling with this question ... http://img86.imageshack.us/img86/2662/picture6fb5.png so far i have only tried part (a), but since i can't see how to do that so far... :( ok so what to do... do we first look at an 'associated problem' ? ... something like...
  13. S

    Solving the Wave Equation PDE: A General Solution Approach

    Hi everyone, I'm having a bit of trouble with this pde problem: http://img243.imageshack.us/img243/9313/picture3ui3.png i get the answer to be u(x,t)=0 but i am guessing that's not right. is the general solution to this problem: u(x,t) = f(x+ct) + g(x-ct) ?? thanks sarah :)
  14. B

    How Do You Solve the Laplace Equation in a Semi-Infinite Strip?

    Hi can someone please help me work through the following question. It is the two dimensional Laplace equation in a semi-infinite strip. \frac{{\partial ^2 u}}{{\partial x^2 }} + \frac{{\partial ^2 u}}{{\partial y^2 }} = 0,0 < x < a,0 < y < \infty The boundary conditions along the...
  15. S

    Solving Drumhead PDE: Normal Modes and Estimation Techniques

    I've searched through about 5 math books but don't know how to start this one: I have a drumskin of radius a, and small transverse oscillations of amplitude: \nabla^2 z = \frac{1}{c^2}\frac{\partial^2 z }{dt^2} Ok, so I can write the normal mode as z=Z(\rho)cos(\omega t)...
  16. I

    How to Solve PDE Problems Involving Wave Equation

    hello, can you guys give me a good resource(websites, etc) on how to solve this type of problem? The thing is, I'm not sure what methods are appropriate for solving this problem. I believe this is a PDE problem involving the Wave equation, but I don't know how to start. I would like to say...
  17. C

    FEM and PDE: Solving a Simple Falling Mass Differential Equation

    i want to understand finite element method by solving the simple differential equation of falling mass d2y/dx2=force/mass eventhough this equation contains derivative of only one variable i want to understand fem using this Or some one can give a somemore difficult pde and solve using...
  18. C

    Finite element-rod elements what is the pde

    case 1)in finite element analysis of structures using simple rod elements we do the stiffness matrix and then find the displacements from loads and constraints case 2)finite element method is a technique for solving partial differential equations. In the case1 what is the partial...
  19. L

    Solving a PDE with ODE: Discontinuity at x=0?

    As part of a separable solution to a PDE, I get the following ODE: X''-rX=0 (*), with -infty<x<infty and the boundary condition X(+/-infty)=0 (X is an odd function here). Thus I have assumed r>0 to avoid the periodic solution, cos. I, therefore, argue that the solution is the symmetric...
  20. Y

    Bounded Solution of the Heat PDE: Is u Necessarily the Heat Kernel?

    Lets say we have a solution u, to the cauchy problem of the heat PDE: u_t-laplacian(u) = 0 u(x, 0) = f(x) u is a bounded solution, meaning: u<=C*e^(a*|x|^2) Where C and a are constant. Then, does u is necesseraly the following solution: u = integral of (K(x, y, t)*f(y)) Where K...
  21. W

    Preparing for a PDE Presentation in 1.5 Weeks

    I have to give a 35-50 minute presentation on PDEs in a week and a half for my class. I really don't have much knowledge of PDE's and I was wondering if anyone knew of any good internet rescourses etc. that would help me get a decent grasp so that I could make a decent presentation and answer a...
  22. L

    Determ the stationary temp with a PDE

    I have a square area with the length a. The temperature surrounding the square is T_0 except at the top where it's T_0(1+sin(pi*x/a)). They ask for the stationary temperature in the area. In other words, how can the temperature u(x,y) inside the area be written when the time = infinity. The...
  23. V

    Fourier/Laplace transform for PDE

    hello i am trying to find the fundamental solution to \frac{\partial c}{\partial t} = D\frac{\partial ^2 c}{\partial x^2} where c=c(x,t) with initial condition being c(x,0)=\delta (x) where \delta (x) is the dirac delta function. i have the solution and working written out in front of me...
  24. H

    Pde problem: inspiration needed

    u_{a}+u_{t}=-\mu t_{u} u(a,0)=u_{0}(a) u(0,t)=b\int_0^\infty \left u(a,t)da Solve u(a,t) for the region a<t Got this question from assignment. My solution is incomplete though, need some inspirations! I have shown that the general solution is u(a,t)=F(a-t)e^{-1/2{\mu}t^{2}} So for...
  25. J

    How Can You Effectively Change Variables to Solve a Specific PDE?

    hi, i am having difficulty trying to find a change of variables to solve this partial differential equation \frac{\partial f}{\partial t} = t^\gamma \frac{\partial ^2 f}{\partial x^2} not sure how to pluck out a change of variables by looking at the equation as its definitely not obvious to the...
  26. S

    PDE with constant coefficient using orthogonal transformation

    Plz Help :( Hi I want 2 know how 2 solve 1st order partial differintial equation (PDE) with constant coefficient using orthogonal transformation example : solve: 2Ux + 2Uy + Uz = 0 THnx :blushing:
  27. M

    Solving the PDE u_xx+u_yy=1 in r<a

    heres the problem: solve u_xx+u_yy=1, in r<a with u(x,y) vanishing on r=a here is what i did, if u_xx+u_yy=1 then u_rr + (1/r)*(u_r) =1 then (r*u_r)_r=r integrating both sides gives r*u_r = (1/2)*r^2+c1 => u_r = (1/2)*r +c1/r, integrating again gives u= (1/4)r^2 +c1log(r) using the...
  28. D

    Classifying a 2nd Order PDE: Understanding the Significance of the Discriminant

    A quick question: When classifying a 2nd order PDE as either Hyperbolic, Parabolic or Elliptic we look at whether the discriminant is either positive, zero or negative respectively. Right. What do we do if the discriminant depends on independent variables (or the dependent variable for that...
  29. V

    Solving a PDE : 2 order in time, 4 order in space, mixed derivatives

    I have a problem that I tried to solve using MAPLE but I guess wasnt doing the right thing. \frac {\partial ^{2} \delta}{\partial t^{2}}+ S*(\frac {\partial^{2}\delta}{\partial \eta^{2}}+M*\frac {\partial^{4}\delta}{\partial \eta^{4}})-G* \frac {\partial ^{3} \delta}{\partial \eta ^{2}...
  30. D

    Can someone help me please?Help Needed: Deriving 4th Order PDE in One Variable

    For some reason i can't post in the calculus and beyond section but i was hoping someone could help me with this question eq.1 du/dt - fv = g*(dn/dx) eq.2 dv/dt + fu = g*(dn/dg) eq.3 du/dx+dv/dg=(1/(H)*(dn/dt) manipulate the equations to derivate a single PDE in one variable n which is...
  31. R

    Solving PDE Linear 1st Order: Help with Colton's Example

    Hi, I'm working through 'Partial Differential Equations, an introduction' by Colton and am not finding it as clear as I hoped to. I'm working through an example on how to solve a linear 1st order PDE. I'll post Colton's example and Italic my questions: Find the GS of xu_x-yu_y+u=x...
  32. R

    What's the best exposition of Partial Differential Equations?

    What's the best exposition of Partial Differential Equations methods at the beginning-graduate level? I've found myself needing Green's functions and such and I don't really know that much about them. Dover reprints would be awesome. Thanks!
  33. S

    Solve PDE: Find u(3/4,2) with l=c=1, f(x)=x(1-x), g(x)=x^2(1-x)

    Find u(3/4,2) when l=c=1, f(x) = x(1-x), g(x) = x^2 (1-x) all i need to do is find the value using d'Alembert's solution of the one dimensional wave. now it is easy for me to extend f(x) for f(x) (-1,0)\Rightarrow \quad x(1+x) (0,1)\Rightarrow \quad x(1-x) (1,2)\Rightarrow \quad...
  34. C

    I forgot how to do my ODES Stuck on a PDE question.

    Let's say I assumed that the answer to a PDE was U(x,t)= XT, where X,T are functions. I then further my answer by getting to a point for T'/T=kX''/X, where k is some constant given in the boundary conditions. I then continue by working on either side to find each function. Suppose I work on...
  35. S

    Solving Laplacian PDE with Separation of Variables

    we are given the laplacian: (d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's u=0 for (-1<y<1) on x=0 u=0 on the lines y=plus or minus 1 for x>0 u tends to zero as x tends to infinity. Using separation of variable I get the general solution u =...
  36. E

    PDE: separation of variables problem

    I am to reduce the following PDE to 2 ODEs and find only the particular solutions: u_tt - u_xx - u = 0; u_t(x,0) = 0; u(0,t) = u(1,t) = 0 I guess u = X(x)T(t), and plug u_tt, u_xx into PDE and divide by u to get: T''/T = X''/X + 1 = K I solve X'' + (1-K)X = 0 first. From...
  37. C

    PDE: If u is a solution to a certain bound problem, question about laplacian u

    Why does the laplacian of u=0 when u is a solution to a certain boundary problem? Is this always the case?
  38. E

    1D wave PDE with extended periodic IC

    I have formula for 1D wave equation: (*) u(x, t) = 1/2 [ f(x + ct) + f(x - ct) ] + 1 / (2c) Integral( g(s), wrt s, from x-ct to x+ct ) I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1 - x). However, for (*) to work, the initial position f(x) and initial velocity...
  39. E

    Solving 1D Wave Equation PDE with f(x), g(x) and nL<=x<(n+1)L

    I have formula for 1D wave equation: (*) u(x, t) = 1/2 [ f(x + ct) + f(x - ct) ] + 1 / (2c) Integral( g(s), wrt s, from x-ct to x+ct ) I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1 - x). However, for (*) to work, the initial position f(x) and initial...
  40. S

    Can this PDE be solved using parametric functions?

    In the HW section, someone proposed: u^2\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0;\quad u(x,0)=x As per "Basic PDEs" by Bleecker and Csordas", treating this as: F(x,y,u,p,q)=0\quad\text{with}\quad \frac{\partial u}{\partial x}=p\quad\text{and}\quad\frac{\partial...
  41. Clausius2

    Mathematica Exploring Parabolic Behavior in PDE Systems: A Mathematical Analysis

    I am looking for an elegant way of demonstrating the parabolical behavior of the system: \frac{\partial u}{\partial x}+\frac{1}{r}\frac{\partial}{\partial r}(vr)=0 u\frac{\partial u}{\partial x}+v \frac{\partial u}{\partial r}=\frac{1}{r}\frac{\partial}{\partial r}\Big(r...
  42. I

    How Can a 3D PDE Be Simplified to a 1D Equation in Theta?

    I got the following PDE: Laplasian[F]+a*d(F)/d(teta)=E*F I worked with cylindrical coordinates (r,teta,z) (teta is the angle between the x-axis and the r vector (in xy plane)) a,E are constants I got the constrains: z=0 r=a , so the whole problem is on a simple ring How can I make...
  43. C

    Resonance pde wave equation u(\phi,t) involving lagrange polynomials

    1/sin(phi) * d/d\phi(sin(phi) * du/d\phi) - d^2u/dt^2 = -sin 2t for 0<\phi < pi, 0<t<\inf Init. conditions: u(\phi,0) = 0 du(\phi,0)/dt = 0 for 0<\phi<pi How do I solve this problem and show if it exhibits resonance? the natural frequencies are w = w_n = sqrt(/\_n) =2...
  44. C

    Q: pde heat eqn u(x,t) history effect \int^t_0 d^2u/dx^2

    How do you solve this type of PDE problem: \int^t_0 e^{-(t-\tau)}\frac{d^2u}{dx^2} d\tau - \frac{du}{dt} = 0 where u(x,0) = sin x Any links or info on this will be appreciated. :
  45. A

    How Can I Solve the Beam Equation using PDEs and the Frequency Domain?

    need to solve the following beam equation: p(x)\frac{d^2\w}{dx^2}-a\frac{d^4\w}{dx^4}-b\frac{d^2\w}{dt^2}=0 don't have experience with pde's, thanks in advance for any hints...
  46. G

    Parabolic PDE in Curved Spaces: Exploring Solutions on Manifolds

    The parabolic approximation was introduced by Leontovich and Fock in 1946 to describe the propagation of the electromagnetic waves in the Earth atmosphera (see Levy M. Parabolic equation methods for electromagnetic wave propagation, 2000). However, the parabolic equation was known long before...
  47. F

    Proving Existence of PDE Solution on H^(-1)(Ω)

    Hello, How can i proof the existence of a solution of a PDE on H^(-1)( Omega)? :mad:
  48. K

    Solving PDE: Is There a General Method or Just Guesswork?

    [SOLVED] Solving PDE I am just wondering, is there any gerneral method in solving PDE's or just by guess works?? thanks...
  49. PerennialII

    Multiphysics PDE solvers with solution dependent domains

    I'm working on solving coupled PDEs (mass diffusion - heat transfer - continuum mechanics) in problems where the solution domain changes depending on the solution (call it an intrinsic coupling if you will). This happens either due to addition of material to the domain or damage of the domain...
  50. B

    Understanding the Validity of PDE Solutions with Variable Substitution

    "Verify that, for any C¹ function f(x), u(x, t) = f(x - ct) is a solution of the PDE u_t + c u_x = 0, where c is a constant and u_t and u_x are partial derivatives." I managed to get the solution for this and a similar problem by showing that the new variable (x - ct in this case) satisfies...
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