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. F

    Complex analysis vs. PDE class

    Im a rising junior in the US starting my upper division physics classes. I have an opening this quarter and want to take an applied math course, but cannot decide between these two: In the mathematics department: "Applied complex anlysis Introduction to complex functions and their applications...
  2. N

    Splitting PDE into system of PDEs

    Hello: I am wondering if there is a general way of splitting the following PDE into two separate equations. I would like to re-write the second-order spatial derivatives on the LHS as first-order derivatives. \[ \frac{{\partial p^2 }}{{\partial x^2 }} + \frac{{\partial p^2 }}{{\partial...
  3. F

    General Solution of PDE yux+xuy=yu+xex: Existence and Infinite Solutions

    find the general solution of yux+xuy=yu+xex ( the solution is in the form of u(x,y)=yex+f(y2-x2)ex ) if at first the value of u(x,y) on the upper half of hyperbola (that is y>=1) has been given as φ,show that if φ has not been given as a special form there is no solution.find that special form...
  4. M

    1st order PDE through Method of Characteristics

    Hello all! I appreciate it if you can share any thoughts that you may have regarding how to solve the following PDE: \frac{\partial U(z,t)}{\partial t}+(1-z)\frac{\partial U(z,t)}{\partial z}=(\frac{1}{z}-1)\left(U(z,t)-U(0,t)\right) Initial condition:U(z,0)=z^{K} U(0,t) arises due...
  5. R

    Ideas for PDE Project (Physiology Theme)

    Hi All, For one of my courses this year (a mathematical modeling course) we have been given a very open ended assignment to go and find some PDE describing ANYTHING in the literature that has an analytical solution and basically go through the solution step by step and present it/explain it...
  6. P

    Solving S.O. PDE by transforming to normal form

    Homework Statement Transform to normal form and solve: 1) u_{xx}+u_{xy}-2u_{yy} = 0Homework Equations Normal form: Au_{xx}+2Bu_{xy}+Cu_{yy}, hence, A = 1, B = \frac{1}{2}, C = -2. Since AC-B^2 = -2.25 < 0 this is a hyperbolic equation. Want to transform it by setting v = \Phi(x,y), z =...
  7. S

    Why is the characteristic of (d/dx) + (d/dt) = 0 not c = x + t?

    Why is the characteristic of (d/dx) + (d/dt) = 0 where d is small delta c = x - t and not c = x + t
  8. P

    MATLAB Solving Nonlinear PDEs in MATLAB: FDM or FEM Method? | Code Included

    I have the following equation to solve: u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx} I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do...
  9. T

    Solving a fourth order PDE by finite difference method by matlab

    Homework Statement how can i solve this problem by MATLAB? pls help me A (d4y/dx4) - B(d2y/dt2) = Cy A=E*I B=p*sin(w*t) c=p*w2 conditions are 1.at x=0, dy/dx=0 2.at x=0,y=0 3.at x=L d2y/dx2=0 4. at x=L d3y/dx3=p (p is a function of t here) x=0 and x=L...
  10. S

    Damped Wave equation, PDE.

    Homework Statement I have the damped wave equation; u_{tt} = 4 u_{xx} -2 u_{t} which is to be solved on region 0 < x < 2 with boundary conditions; u(0,t) = 2, u(2,t) = 1. i must; 1) find steady state solution u_{steady}(x) and apply boundary conditions. 2) find \theta(x,t)...
  11. G

    Difficulties with solution/plotting of a PDE.

    Homework Statement Question attached Homework Equations The Attempt at a Solution I'm mostly wondering with c) and also want to check if my solution is correct. My solutions for this question are: u(x,t)= -1/2 for x <= -1/2*t = 1 for -t < x < 1-t = 1/2 for x =>...
  12. Y

    Solving Klein-Gordon PDE w/ Change of Variables

    Hi. I'm following the solution of a Klein-Gordon PDE in a textbook. The equation is \begin{align} k_{xx}(x,y) - k_{yy}(x,y) &= \lambda k(x,y) \\ k(x,0) &= 0 \\ k(x,x) &= - \frac{\lambda}{2} x \end{align} The book uses a change of variables $\xi = x+y$, $\eta = x-y$ to write \begin{align}...
  13. W

    Solve a system of second order PDE

    I need to solve the following system of differential equations: \frac{\partial^2 y}{\partial t^2} + A\frac{\partial y}{\partial t} - B \frac{\partial^2 y}{\partial z^2} = Cq \frac{\partial^2 q}{\partial t^2} + D\frac{\partial q}{\partial t} + q = E\frac{\partial^2 y}{\partial t^2}...
  14. B

    Solving 1st Order PDE with Initial Condition - Help Needed

    I'm trying to solve this equation: Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0 I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...
  15. M

    Need help with PDE application's in mechanic

    I need to know some of the application of partial differential equation in mechanic ? just need some headlines and I 'll Google them . thanks
  16. D

    Graduate level PDE important in applied math?

    Dear Mathematicians and Physicists, In light of the coming fall semester, I am having a decision to take a full blown graduate level Elliptic PDE class. The prerequisites is of course Graduate level analysis and perhaps a undergrad class in PDE, both of which I already have. The class will be...
  17. N

    Mass conservation in radially symmetric parabolic PDE problems

    Dear all, I'm trying to solve the 2d heat equation in a radially symmetric domain, numerically using the Crank-Nicolson method. i.e. \dfrac{\partial u}{\partial t} = D\left( \dfrac{\partial^2u}{\partial r^2}+\dfrac{1}{r}\dfrac{\partial u}{\partial r}\right) Applying the Crank-Nicolson...
  18. MathematicalPhysicist

    Mathematica Plotting PDE by using Mathematica.

    Hi, I have this problem, I need to plot the solution of the next nonlinear-PDE problem: y_{tt}=((y_x)^3)_x+y^3-y where y=y(x,t), and we are looking for a solution with a compact support in (-x0,x0) (which I need to find x0), i.e the solution vanishes for x>=x0 or x<=-x0, and also y=y_x=0 on...
  19. O

    Confused about the terminology for the domain pde

    Homework Statement δu/δt+2tδu/δx=1 for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0 Homework Equations The Attempt at a Solution ((dx)/(dt))=2t x=t²+c x-t²=c the general solution is: u=t+F(x-t²) Now i am...
  20. T

    Transforming PDE to ODE: How Can We Subsitute Correctly?

    From PDE to ODE ?! + research Homework Statement In the attached research, What are the steps that we work to transform the equation (1) to (8) Homework Equations (1) and (8) The Attempt at a Solution I know that they used similarity transformations but I do not know how to do...
  21. 5

    Do I need ODE and PDE for differential topology?

    I am a senior in mathematics studying graduate point-set topoology atm. I am thinking I want to study differential topology in graduate school and maybe apply it to problems in cosmology. Do I need to take more ODE and PDE? I took intro to diff eq- the one that all engineering undergrads take...
  22. B

    Why Is the Characteristic Equation Crucial in Solving PDEs?

    I'm following an algorithm my teacher gave us and I'm trying to understand it... I'm trying to solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0 First I need to solve the homogeneous equation. So I set up the relation: V(y)=U(2y+c, y) to solve 2Ux-Uy=0 where the characteristic equation is y=1x/2...
  23. S

    Any hope for this PDE? Diffusion in population genetics

    I'm working on a problem in multi-allele diffusion in population genetics and I have come to this PDE: 0 = (tp_1(1-p_1)-sp_2)\frac{\partial u}{\partial p_1}+(sp_2(1-p_2)-tp_1)\frac{\partial u}{\partial p_2} + \frac{p_1(1-p_1)}{2}\frac{\partial^2 u}{\partial p_1^2} +...
  24. B

    Help with first integral of PDE

    Hey guys, I'm having a little difficulty with a pde I'm trying to solve. It boils down to solving for a first integral. I don't want the answer, but I'd be glad to get a little help. We have the system: \frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{xy(z^2 + 1)} We can use the first two and find...
  25. W

    Solving Diffusion PDE in a Hollow Cylinder

    Dear all, I'm trying to solve the diffusion PDE for my system, shown below: \frac{\partial C}{\partial t} = D (\frac{\partial^2 C}{\partial r^2} + \frac{1}{r} \frac{\partial C}{\partial r}) where C is the concentration, changing with time t and radius r. D is the diffusion...
  26. M

    Solving the PDE 1-d Heat Equation for a Flipped Rod

    regarding 1-d Head Equations on rods. I am aware of how to long a rod with length x=0 to x=L. and initial conditions of u(0,t)=0 degrees and u(L,t)=100 degrees. But how does the problem change if before t=0 the rod at x=0 was at 100 degrees and x=L was at 0 degrees. So at time=0 the rod was...
  27. T

    The physical meaning of the PDE?

    the physical meaning of the PDE?! Homework Statement http://agentsherrya.jeeran.com/qu.JPG Homework Equations How can I know the physical meaning of the following partial differential equation?!
  28. T

    Linear 1st order PDE (boundary conditions)

    Homework Statement Solve the equation u_{x}+2xy^{2}u_{y}=0 with u(x,0)=\phi(x) Homework Equations Implicit function theorem \frac{dy}{dx}=-\frac{\partial u/\partial x}{\partial u/\partial y}The Attempt at a Solution -\frac{u_x}{u_y}=\frac{dy}{dx}=2xy^2 Separating variables...
  29. Y

    Is D'Alambert solution important for studying PDE?

    I want to know is it important to study D'Alembert solution? My main goal is to study Electromagnetics and wave equations, not the mechanical or heat equations. Seems like it is just one way of solving the PDE.
  30. P

    How Do You Solve a Second-Order Linear PDE with Given Boundary Conditions?

    Finding basic solutions to a PDE?? So the problem is: x_o=0 \varphi'' + 4\varphi' + \lambda\varphi=0 which satisfies \varphi(0)=3 and \varphi'(0)=-1 I really don't even know where to start, I think its like an ODE right where we assume a solution, usually sin or an exponential and plug...
  31. N

    Green's function for homogeneous PDE

    Hi there, could anyone help me on this particularly frustrating problem I am having... I have a linear parabolic homogeneous PDE in two variables with a boundary condition that is a piecewise function. I can solve the pde (with a homogeneous BC) however trying to impose the actual BC makes...
  32. G

    Solving PDE with Analytical Solution: Exploring LaTex Code and Techniques

    LaTex Code: \frac{\partial U}{\partial t} + ax\frac{\partial U}{\partial x} + b\frac{\partial^2 U}{\partial x^2} = 0 Can someone please tell me how to solve this PDE? Thanks, Geoff
  33. Y

    What Does the Notation \(\frac{\partial u}{\partial t}(x,0)\) Indicate in PDEs?

    What is the meaning of \;\;\frac{\partial u}{\partial t}(x,0) Is it equal to \;\;\frac{\partial u(x,t)}{\partial t}\;\;first\;then\;set\;t=0 or \;\;\;\frac{\partial u(x,0)}{\partial t}\;\; Which is setting t=0 in u(x,t) first then differentiate?
  34. R

    PDE U_t = aU_xy (mixed derivatives)

    I am trying to solve (1) U_t = 2bU_xy (as part of U_t = aU_xx + 2bU_xy + cU_yy) using centred finite difference method. When a > 0 everyhing is OK but when a < 0 I get some oscillation problems. My questions are: 1. is there a pde theory for (1)? 2. what is the 'motivation' for (1)...
  35. Y

    Need to check the answer of some simple PDE

    I don't have the answer of these question. Can someone take a look at a) and tell me am I correct? I don't even know how to solve b) a)Homework Statement a) Show u(x,t)=F(x+ct) + G(x-ct) is solution of \frac{\partial^2 u}{\partial t^2}= c^2\frac{\partial^2 u}{\partial x^2} The...
  36. B

    PDE: The Eikonal Equation method of characterstics, etc.

    Homework Statement I need to solve the Eikonal Equation c^2(u_x^2 + u_y^2) = 1 Initial condition u(x,0) = 0 C(x,y) = |x|, but x>0 to essentially C = x Oh. And the solution is given as \ln{\frac{\sqrt{x^2 + y^2} + y}{x}} Homework Equations None other than the usual method of...
  37. Z

    Somie info about this PDE please ?

    Somie info about this PDE please ?? \frac{\partial u}{\partial t} = r u - (1+\nabla^2)^2u + f(u) where f(u) is an smooth function , u=U(x,t) is the solution of the PDE this is the Swift-Hohenberg equation, my teacher has asked me to solve it or look some info about it specially -...
  38. K

    MATLAB Help, solving simple PDE with ODE45 or ODE23 solver in matlab

    guys please help me, I'm trying to solve a simple moving PDE equation in matlab. The equation I'm trying to solve is dq(x,t)/dt=-c*dq(x,t)/dx with initial condition for example q(x,0)=exp(-(x-5)^2) c is a constant. What i want to do is to first discritize the initial condition with...
  39. A

    How Can Surface Evolver Software Help in Solving PDEs?

    Hello friends please attached file to see my problem
  40. J

    Next set of PDE, which presents fluid flow

    Hallo, I must solve next set of PDE, which presents fluid flow. dP/dx=d/dx(mi*dv/dx)+d/dy(mi*dv/dy) dP/dy=d/dx(mi*du/dx)+d/dy(mi*du/dy) where mi=const with BC: v=v at x=0 u=u at y=0 Can you give me some hint? thanks j.
  41. R

    2 dimensional PDE and a higher dimension problem.

    Homework Statement The 2d PDE Assume f\in S(\mathbb{R}^2) (Schwartz space) Then solve u_{xx}(x,y) + 2u_{yy}(x,y) + 3u_{x}(x,y) -4u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 u_{xxxx}(x,y) - u_{yy}(x,y) + 2u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 Homework Equations The relevant...
  42. R

    PDE Math Homework Help: Solving BVPs for Periodic Functions

    Homework Statement We are given f \epsilon C(T) [set of continuous and 2pi periodic functions] and PS(T) [set of piecewise smooth and 2pi periodic functions] SOlve the BVP ut(x,t) = uxx(x,t) ; (x,t) belongs to R x (0,inf) u(x,0) = f(x) ...
  43. P

    Solution of the 2nd-order pde u_t=u_xy

    hey guys, i've reduced a more complex pde to the second-order linear equation u_t=u_xy, but now I'm a bit stuck! firstly, does anyone know if this equation has a proper name and thus been studied somewhere in the literature? secondly, any ideas on how to proceed with the general...
  44. E

    How to Solve a First-Order Nonlinear PDE using the Method of Characteristics?

    i have to solve this equation : du/dx * du/dy = x*y u(x,y) = x for y =0 with putting this equation in the form : F(x,y,u,du/dx,du/dy) = 0 . it can be solved. But mine book does not explain how to do this, there are no examples. Can someone help me ? or any links of examples on the...
  45. A

    Can the Herring-Trilling Equation Be Solved Numerically?

    Hi all, I'm a graduate student of engineering and have some knowledge of solving ODEs and PDEs - usually enough to do the simulations I need. However, I'm currently stumped by a PDE I found in a paper. I've attached the PDE in question (the Herring-Trilling equation) to this post. I'm...
  46. J

    Solving PDEs with IC, BCs: Help from Kevin

    Hi: I have the following PDE: ytzz=yzzzz+delta(t) With I.C.: t=0, y=0; and B.C.s: z=0, y=0,yzz=0; z=-x,y=0,yz=0 Can someone show me how to solve it? Kevin
  47. M

    What is (∂u ∕∂x)dx in the expression for mass flow rate?

    Hi I have seen the expression for mass flow rate in one of the problems I am working on. I used to simply apply the expression for calculating the mass flow rate with respect to the position as (ρu + (∂u ∕∂x)dx) dy dz). ρ, u are density and velocity component respectively. I would like to...
  48. R

    PDEs, Manifolds & Frobenius: Intro Course Insights

    I'm looking to delve into PDEs. I'm reading thru Lee's Smooth Manifolds, and he has a chapter on integral manifolds, and how they relate to PDE solutions via Frobenius' theorem. I find the hint of geometrical aspects very appealing. Evans' PDE book (that I was planning on picking up)...
  49. L

    Zombie PDE Model: Creating a Theoretical Outbreak

    Hey guys, I'm currently taking a Partial Differential Equations class, and for one assignment we have to come up with a model for a theoretical zombie outbreak. Well anyways, this is what I have gathered thus far: - I am defining my u(r,z,t) to be the population density of humans, where...
  50. X

    Simplifying the Chain Rule for Partial Derivatives in PDEs

    If z = f(x,y) and x = r \cos{v}, y = r\sin{v} the object is to show that d = \partial since it's easier to do on computer Show that: \frac{d^2 z}{dr^2} + \frac{1}{r} \frac{dz}{dr} + \frac{1}{r^2} \frac{d^2 z}{dv^2} = \frac{d^2 z}{dx^2} + \frac{d^2 z}{dy^2} It's from Adams calculus, will...
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