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. N

    Solving a Homogeneous PDE with u_{xxx} - 3u_{xxy} + 4u_{yyy} = e^{x+2y}

    Homework Statement u_{xxx} - 3u_{xxy} + 4u_{yyy} = e^{x+2y} The Attempt at a Solution Ok so I tried doing the following to solve the homogeneous equation \begin{align*} u_{xxx} + u_{xxy} - 4u_{xxy} + 4_{yyy} = 0 \\ [d^{2}x(dx -dy) - 4dy(dx + dy)(dx -dy)]u = 0 \\ [(dx -...
  2. D

    Math Courses Relevant to General Relativity

    I'm a rising math major with a developing interest in General Relativity. I think the idea of studying Relativity from a mathematicians perspective sounds very appealing for graduate work. Besides differential geometry and partial differential equations, what are the most relevant pure math...
  3. Q

    My question is about solving a Quasilinear PDE without a shock

    Homework Statement Solve \frac{\partial \phi}{\partial t} + \phi \frac{\partial \phi}{\partial x} - \infty < x < \infty , t > 0 subject to the following initial condition \phi (x,0) = \left\{ \begin{array}{c} 1,\; x<0\\ 1-x,\;0\leq x<1\\ 0,\; x\geq1\end{array}\right. Homework...
  4. S

    How Do You Solve a PDE Model Similar to the Heat Equation?

    Hello, I derived a model in the form \begin{array}{rcl}\frac{\partial U(\vec{x},t)}{\partial t}&=&\gamma^2\Vert\nabla U(\vec{x},t)\Vert,\\\int_{\Omega}U(\vec{x},t)\, d \Omega&=&U_0,\quad\forall t\\U(\vec{x},0)&=&f(\vec{x}).\end{array} I don't know to solve that. THanks for help.
  5. C

    Explicitly Solving a PDE: Is There a Solution?

    I just had a 'quiz' in my PDE class today and there was a problem my friends and I are convinced has no explicit solution. I want to know if maybe we are doing something wrong? Homework Statement (x+y)u_{x} + yu_{y} = 0 [/itex] u(1,y) = \frac{1}{y} + ln(y) [/itex]Homework Equations ...The...
  6. S

    1st order PDE, quadratic in derivatives, two variables analytic solution?

    I have the PDE: (v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z). I have some boundary conditions, of sorts: p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity p=0 at f=r, where (f_r)^2=p*r/v-v*v_r (f_z)^2=p*r/v+v*v_r Is it possible that one could obtain an...
  7. G

    Can PDEs be solved using ODEs in quantum mechanics?

    Here's my question: as soon as I learned Quantum Mechanics and Schrodinger equation, I saw a "similarity" with the equation one gets in classical mechanics for the evolution of a function in phase space. In QM one has: i\hbar\frac{d}{dt}\psi = \hat{H}\psi and this is a evolution...
  8. E

    What Do ODE, PDE, DDE, SDE, and DAE Stand For?

    Okay, kind of a silly question...but what do all of these stand for? ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on this stuff) PDE=Partial Differential Equations ( Hope this is right too, taking this next semster) DDE=...? SDE=...? DAE=...
  9. L

    Solve PDE Method of Characteristics help

    The problem: Solve for u(x,y,z) such that xu_x+2yu_y+u_z=3u\; \;\;\;\;u(x,y,0)=g(x,y) So I write \frac{du}{ds}=3u \implies \frac{dx}{ds}=x,\; \frac{dy}{ds}=2y\;\frac{dz}{ds}=1 . Thus u=u_0e^{3s},\;\;x=x_0e^{s}\;\;y=y_0e^{2s}\;\;z=s+z_0 but from here I can't figure out what to do, there...
  10. M

    Use Fourier transform to solve PDE damped wave equation

    This question is also posted at http://www.mathhelpforum.com/math-help/f59/use-fourier-transform-solve-pde-damped-wave-equation-188173.html Use Fourier transforms to solve the PDE \displaystyle \frac{\partial^2 \phi}{\partial t^2} + \beta \frac{\partial \phi}{\partial t} = c^2...
  11. S

    Solve Heat Equation PDE with Boundary Conditions

    Homework Statement u_{t}=3u_{xx} x=[0,pi] u(0,t)=u(pi,t)=0 u(x,0)=sinx*cos4x Homework Equations The Attempt at a Solution with separation of variables and boundry conditions I get: u(x,t)= \sumB_{n}e^-3n^{2)}}*sinnx u(x,0)=sinx*cos4x f(x)=sinx*cos4x=\sumB_{n}*sinnx...
  12. D

    PDE: Laplace's Equation solutions

    Homework Statement Suppose that u(x,y) is a solution of Laplace's equation. If \theta is a fixed real number, define the function v(x,y) = u(xcos\theta - ysin\theta, xsin\theta + ycos\theta). Show that v(x,y) is a solution of Laplace's equation. Homework Equations Laplace's equation...
  13. L

    Help with simplifying a 2nd order pde

    I was given the equation dp/ds = 4 + 1/e*d/de(e*dp/de) The derivatives in the equation are partial derivatives the values of p,s,e are dimensionless numbers. I am to assume that the solution is separable and then use finite difference method to solve for p, the finite difference method...
  14. H

    Solving the Unknown in PDE: Finding u_B!

    unknown in PDE! Hi, I'm solving a problem which determines the flow between a porous material and an impermeable material, using the slip-flow boundary conditions as proposed by Beavers and Joseph in '67. I can solve the whole problem as stated below, which gives the velocity u of the fluid...
  15. M

    Cant understand similar proof Quantum numbers from PDE (pdf attachment)

    I believe that this is similar to the proof of schrodinger equation to obtain quantum numbers, however i cannot seem to understand the relationship between n, l and m: I have attached a pdf file on partial differential equations and on page 5, i cannot seem to understand why it is +n^2 and...
  16. G

    Solving a PDE with Characteristic Curves and Initial Conditions

    Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...
  17. C

    First order linear PDE, understanding solution/method

    Homework Statement Solve the initial boundary value problem: u_t + cu_x = -ku u is a function of x,t u(x,0) = 0, x > 0 u(0,t) = g(t), t > 0 treat the domains x > ct and x < ct differently in this problem. the boundary condition affects the solution in the region x < ct, while...
  18. F

    Solve Cauchy Problem for PDE: exp(-x)dz/dx+{y^2}dz/dy=exp(x)yz

    Hi guys tryin to study for a pde exam and cannot solve this question Find a general solution of the equation exp(-x)dz/dx+{/y(squared)}dz/dy=exp(x)yz (ii) Solve the Cauchy problem, i.e. find the integral surface of this equation passing through the curve . y = ex/3 , z = e ...
  19. S

    Integrating Second-Order PDE: u''(x) = -4u(x), 0 < x < pi | Calculus Help

    1. Integrate (by calculus): u''(x) = -4u(x), 0 < x < pi 2. The attempt at a solution I'm not really sure where to start on this one is my problem. I can see that it won't be a e^2x problem because of the negative, which leads me to believe that it will deal with the positive/negative...
  20. D

    How many B.C. are necessary for first order PDE set?

    Hi I have a set of two linearized integro-partial-differential equations with derivatives of first order (also inside the integrals). How many boundary (initial) conditions should I give for such problem for the solution to be unique? is the 'initial condition that intersect once with the...
  21. S

    Solving a Higher-Order PDE: Traveling Wave & Phase Portrait

    Homework Statement Consider the PDE ut + 6u3ux + uxxx = 0 which may be thought of as a higher-order variant of the KdV. a) Assume a traveling wave u = f(x-ct) and derive the 3rd-order ODE for that solution. b) Reduce the order of this ODE and obtain the expression for the polynomial g(f)...
  22. H

    Solving a PDE using multiple transforms

    Suppose I have the PDE: \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=\frac{1}{c^{2}} \frac{\partial^{2}u}{\partial t^{2}} with u(0,x,y)=\partial_{t}u(0,x,y)=0 along with u(t,0,y)=f(y) With x\geqslant 0. My initial thoughts were to take the Laplace transform in t...
  23. B

    Determine the general solution of QL PDE

    Homework Statement 1) Determine the general solution of the equation 2) Use implict differentiation to verify that your solution satisfies the given PDE Homework Equations u u_x-y u_y=y The Attempt at a Solution \frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y} Take the second two...
  24. T

    Characterisitics of a Parabolic PDE

    Greetings, I want to find the characteristics of the following parabolic PDE u_t + v u_x + w u_y + a(t, x,y,v,w, u) u_v + b(t, x,y,v,w, u) u_w - u_{vv} - u_{ww} = c(t,x,y,v,w,u) Where u=u(t,x,y,v,w) I know how to find the characteristics of a 2nd-order one-dimensional PDE. I also know how...
  25. C

    Finding a solution of this PDE

    Hi, i'm having trouble finding a solution to this PDE, \frac{d U(x,y,t)}{dt} = A(x) \frac{\partial U(x,y,t)}{\partial y} + B(y) \frac{\partial U(x,y,t)}{\partial x} with only knowledge of the initial condition U(x,y,0)=F(x,y). I've tried to solve this using characteristics but the...
  26. F

    Mathematica Wave eqaution PDE in mathematica

    hi i can't make DSolve solve the wave equation with simple bvc ive gone through the mathematica documentation and can't find the answer for the input \text{DSolve}\left[\left\{u^{(2,0)}[x,t]==4 u^{(0,2)}[x,t],u[x,0]==1,u^{(0,1)}[x,0]==\text{Sin}[x]\right\},u,\{x,t\}\right] it just...
  27. I

    Solving second order CC non-homogenuous pde

    Homework Statement Uxx+Uyy-c^2*u=0 for -inf<x<inf y>0, subject to boundary conditions Uy(x,0)=f(x), u(x,y) bounded as x-> +/- inf or y -> inf Homework Equations Fourier transform greens function? The Attempt at a Solution I would think that I would have to go through two...
  28. S

    Homogenous PDE with separation of variables

    Homework Statement Sorry don't know how to use the partial symbol, bear with me partial u wrt t=2*(2nd partial u wrt x) Boundary conditions: partial u wrt x (0,t)=partial u wrt x (1,t)=0 Initial conditions u(x,0)=x(1-x) Homework Equations I get an answer that is different...
  29. Z

    Analysis of spatial discretization of a PDE

    Hi everybody, I hope I am asking in the right forum. Let describe the problem as follows: I have a 1D heat equation. To solve it, I use finite-difference method to discretize the PDE and obtain a set of N ODEs. The larger N gives the better solution, i.e., the closer the solution to the...
  30. C

    How do I go about solving this PDE?

    Homework Statement \frac{\partial^2X}{\partial a^2} + (X^4-1)\frac{\partial X}{\partial a} = 0 Homework Equations How do I go about solving this PDE ? The Attempt at a Solution Please help !
  31. C

    Solving PDE: How to go about it?

    Homework Statement 2\frac{\partial^2X}{\partial a \partial b} + \frac{\partial X}{\partial a}(x^4-1) = 0 Homework Equations How do I go about solving this PDE ?? The Attempt at a Solution Please help !
  32. I

    Help solving 1st order PDE with associated Equation

    Homework Statement Solve This equation: \epsilon(Ut+Ux)+U=1 with \epsilon being a very small number from 0 to 1 and x bounds from neg infinity to pos infinity, t>0, and condition u(x,0)=sinxHomework Equations method of associated equation (dx/P=dt/Q=du/R, and so forth)The Attempt at a Solution...
  33. S

    Can Nonlinear PDEs Be Solved with Newton's Method in n-Dimensional Domains?

    For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n, Q.1 do you have some ideas of the existence conditions of following PDE: a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product; b) U >=0 Does it need a first type or second type of boundary...
  34. jaketodd

    Trying to get this PDE in terms of 'y'

    I will love forever whoever can show me the steps of how to get the following equation in terms of y=[...] This is not a homework question. I have a calculus book that has given me some progress, such as expanding the equation to a mixture of terms and first order partial derivatives, and I...
  35. S

    PDE : Can not solve Helmholtz equation

    PDE : Can not solve Helmholtz equation (This is not a homework. I doing my research on numerical boundary integral. I need the analytical solution to compare the results with my computer program. I try to solve this equation, but it not success. I need urgent help.) I working on anti-plane...
  36. R

    PDE problem, Solve using Method of Characteristics

    Hi This problem occurred on my final and I could not figure it out. Homework Statement The problem was a partial differential equation (I forgot the exact equation) but the solution was a hyperbolic function in the form of u(x,y)= f(x+y) + g (x+y), it was part b that gave me the...
  37. G

    Cauchy vs. Dirichelt/Neumann Condition for PDE

    Hi, Can anybody tell me the difference between a Cauchy Boundary condition and a combined Dirichlet/Neumann Boundary Condition for PDEs? The reason why I'm asking is because Cauchy boundary conditions can be used to solve Open Hyperbolic PDEs, whereas Dirichlet/Neumann can only be used to...
  38. D

    Sounds like a retardedly basic PDE problem

    Homework Statement This is a simple pde I need to solve in order to determine a straightforward expansion for a given overall equation. Homework Equations \partialu/\partialx+\partialu/\partialy=0 with initial condition: u(x,0)=epsilon*phi(x) The Attempt at a Solution I...
  39. Q

    Solving 2nd Order PDE for dx/ds in d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0

    Homework Statement Need to solve for dx/ds in the following equation, keeping dy/ds. Homework Equations d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0 The Attempt at a Solution I can just rearrange to get: dx/ds = (y/2)(ds/dy)(d^2x/ds^2) But, this is not clean to use for some later...
  40. H

    How Do You Solve a PDE with Time-Dependent Boundary Conditions?

    Hi I need help to solve this partial differential equation. ∂C/∂t=D((∂^2 C)/(∂r^2 )), boundary conditions, C = Co a t r = a(t) C = 0 at r = b(t) Initial Conditions, C = Co...
  41. N

    Solving pde with gaussian function

    I just developed this model to describe an ecological process but have trouble solving the equation. My first question is: is the form even analytically solvable? And if so, what steps / references should I resort to? 'a', 'delta' and 'sigma' are all constants. *Current reference book...
  42. N

    Is this pde analytically solvable?

    I'm a theoretical biologist in the process of developing a spatial model for animal movement. So far, I've arrived at the following structure of an equation (see attachment): *theta is just some function of x and t. Having never formally studied pde, I'm wondering whether one can, from this...
  43. Saladsamurai

    PDE: Sep of Vars Non homogenous BCs

    Homework Statement I have Laplace's equation that I need to solve. I was told that it can be solved by separtion of variables and that it should yield sinh and cosh solutions. As it stands, my current set of BCs are not homogeneous. So I need to find the proper way to assume my solution...
  44. P

    Second-order, linear, homogeneous, hyperbolic PDE. Solvable?

    First, my deepest apologies if I am asking a trivial question, or asking it in the wrong forum. I am trying to solve a PDE, which I have already reduced to canonical form and simplified to the full extent of my abilities. The PDE is: u_xy + a(x,y) u_x + b u_y = 0, with a(x,y)=2/(x+y) and...
  45. A

    Why dummy variables used for the coefficients of a PDE solution?

    have been solving PDEs by sep of variables, and the solution that comes out is generally a summation the general look of it is something like: U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t The above may not be exactly right, I was thinking along the lines of heat equation where...
  46. B

    Solution to pde with directional derivative first order

    Homework Statement trying to solve v.\nabla_x u + \sigma(x) u = 0 (x,v) \in \Gamma_- \Gamma_- = \left\{(x,v) \in X x V, st. -v.\nu(x) > 0\right\} \nu(x) = outgoing normal vector to X v = velocity u = density g(x) = Incoming boundary conditions The Attempt at a...
  47. J

    Solving Inhomogeneous Wave PDE with Separation of Variables on (0,pi)

    Problem: Use separation of variables to solve utt = uxx-u; u(x, 0) = 0; ut(x, 0) = 1 + cos3 x; on the interval (0, pi), with the homogeneous Dirichlet boundary conditions. Question: I know how to use separation of variables, but can`t figure out what to do with the u in the...
  48. C

    Solving Diffusion PDE By Finite difference Method in fortran

    Hey, I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper...
  49. S

    Separation of Variables for a PDE

    Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...
  50. maverick280857

    How to Solve a Complex 2D PDE in Toroidal Coordinates?

    Hi, After considerable simplification in a problem I'm working on, I end up with the following partial differential equation: \partial_{\eta}\left(\frac{\sinh\eta}{\Delta}\partial_{\eta}g\right) + \partial_{\theta}\left(\frac{\sinh\eta}{\Delta}\partial_{\theta}g\right) + c^2\left[\frac{E_{p}...
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