Pdes Definition and 148 Threads

Hello Fellow Physics People, I am just now taking a math methods course for Physicists and we're using Mary Boas book. I wanted to supplement it for better understanding as saw Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow. Reading reviews for this book on...

Hi Forum, I'm trying to use Mathematica to graphically explore a system of four PDEs, as defined in Yang et al. (2002). Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes. Physical Review Letters 88(20). The equations are: \frac{\partial...

Question about Solutions of second order linear PDEs I don't have very much formal knowledge of this topic, this is something I have been thinking about, so excuse me if my notation is off. I have a question about second order linear PDEs, do all have a separable solution? It seems that we can...

Hi, I need a book that I can use for reference to solve any Partial Differential Equation imaginable, if it has a solution of course. Can you suggest me any?

I'm wondering if people have recommendations on this topic. It's something I've been meaning to tackle for a long time now. I'm interested in learning how to solve PDEs as well as learn about uniqueness theorems and such. The more rigorous the book is, the better. I already have good...

I have two more loosely based questions about PDEs and the separation of variables technique: In the intro of this chapter the author imposed that we "assume" the the solution to a set of special PDEs is: U(x,t) = X(x)T(t) where X and T are the eigenfunctions. My question is how did...

Homework Statement Show that there is no solution for the system u_x - 2.999999x^2 y + y = 0, u_y - x^3 + x = 0. Homework Equations The Attempt at a Solution I took the first equation and integrated w.r.t x, then differentiated w.r.t y. But I'm not sure if it helps: u_y -...

So we just started finding general solutions for homogenous&linear two-variabled PDEs by using separation of variables in my engineering-math class. There the professor tells us to assume the solution of a PDE is in the form of F(x)*G(t). But when is the solution in the form of F(x)*G(t)? When...

Hi all, I understand some PDE is linear like \frac{\partial f}{\partial t}+\frac{\partial f}{\partial x}=0 while some PDE is nonlinear like \frac{\partial f}{\partial t}+f\frac{\partial f}{\partial x}=0 Some PDE is weak nonlinear and some is strong nonlinear. I am wondering whether...

Is there a hole in knowledge as to the origins of PDEs? If there is a void, is Schwartz space a suitable basis? Schwartz spaces are intermediate between general spaces and nuclear spaces. Infra-Schwartz spaces are intermediate between Schwartz spaces and reflexive spaces.

I have established existence and uniqueness of solutions to a nonlinear elliptic system of PDE's and would like to see how the solutions look like numerically. I have some programming background on MatLab and C++. I also understand basic ODE numerical schemes. But I am not so sure, if I need to...

Hi all, first post :) I have a system of z-propagated nonlinear PDEs that I solve numerically via a pseudo-spectral method which incorporates adaptive step size control using a Runge-Kutta-Fehlberg technique. This approach is fine over short propagation lengths but computation times don't...

Suppose we have two multivariate functions, u_{1}(x,t) and u_{2}(x,t). These functions are solutions to second-order linear equations, which can be written as follows: Au_{xx}+Bu_{xy}+Cu_{yy}+Du_{x}+Eu_{y}+Fu=G Each of the coefficients are of the form A(x,y). Now, the linearity of these...

This is actually a request, I don't know if these are the correct forums for me to post these kinds of things, but yeah. Alright. I intended to study and learn numerical methods with PDEs on my own. And sadly the only thing I can comprehend is the Liebmann method. :cry: And I got so little...

Is there a way to "crudely" approximate PDEs with Fourier series? By saying crudely, I meant this way: Assuming I want a crude value for a differential equation using Taylor series; y' = x + y, y(0) = 1 i'd take a = 0 (since initially x = 0), y(a) = 1, y'(x) = x + y; y'(a)...

I'm trying to write a very simple program to generate shear and bending moment diagrams for beams. The thing is that I don't know what kind of loading that the beam may see so I want to be able to write it as generically as possible. I'm trying to find a web resource (not a book, unless...

You can find problems with downloadable notebooks now http://www.mathhelpboards.com/f49/engineering-analysis-notes-2882/. If one boundary is insulated and the other is subjected to and held at a temperature of unity, we wish to determine the solution for the transient heating of the slab. The...

Homework Statement How were the integral lines dt/a = dx/b derived from the PDE aUt + bUx = 0 where Ut is the partial derivative with respect to time and Ux with respect to x and a, b are constants. Homework Equations I honestly have no idea. I may be unprepared for this course as...

Homework Statement I'm doing a course on numerical solutions of PDE and I am waaaay out of my depth, having not covered differential equations previously. I spoke to my lecturer about this and he said I would be fine as the course is on FDM/FEM and not analytic solutions but this is week 4 and...

I am working on a dual undergrad degree program, with my primary degree being Electrical Engineering. This fall will start the last semester to get my B.S. in Math completed. For the engineering side I am taking Electromagnetics and Signals and Systems Analysis this semester. I need only to...

Homework Statement Show that the wave equation u_{tt}-\alpha^{2}u_{xx}=0 can be reduced to the form \phi_{\xi \eta}=0 by the change of variables \xi=x-\alpha t \eta=x+\alpha tThe Attempt at a Solution \frac{\partial u}{\partial t}=\frac{\partial \xi}{\partial t}\frac{\partial...

Hi I am looking for a good book on PDEs. By good, I mean geometrically intuitive. Something like H M Schey's book on vector calculus. I know a bit about solving PDEs, I know they are elliptic, hyperbolic or parabolic, characteristic equation defines the type & that's just about it. What I am...

Hello, this is my first post! I am interested in studying PDEs (heat/wave equations, etc.). At my university, the only listed prereq. for PDEs is ODEs, which can be taken after Calc II. So, essentially, one could enroll in PDEs without taking Calc III, but I am not sure if that would be...

Hi, I am trying to simplify the following equations to get a relationship involving just \eta : 1) \nabla^2 \phi(x,z,t) = 0 for x\in [-\infty,\infty] and z\in [-\infty,0] , t \in [0,\infty] subject to the boundary conditions 2) \phi_t+g \eta(x,t) = f(x,z,t) at z=0 3)...

1) Solve $\begin{aligned} {u_t} &= K{u_{xx}},{\text{ }}0 < x < L,{\text{ }}t > 0, \\ u(0,t) &= 0,{\text{ }}u(L,t) = 0,{\text{ for }}t > 0, \\ u(x,0) &= 6\sin \frac{{3\pi x}}{L}. \end{aligned} $ 2) Solve $\begin{aligned} {u_t} &= 4{u_{xx}},{\text{ }}0 < x < 1,{\text{ }}t > 0, \\...

Hey all, I was reading up on Harmonic functions and how every solution to the laplace equation can be represented in the complex plane, so a mapping in the complex domain is actually a way to solve the equation for a desired boundary. This got me wondering: is this possible for other PDEs...

1) $u_x+u_y=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=\cos x,\,x\in\mathbb R.$ 2) $xu_x+u_y+uy=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=F(x),\,x\in\mathbb R.$ 3) Solve the following equation $2xu_y-u_x=4xy,$ where the initial curve is given by $x=0,\,y=s,\,z=s.$ ------------------------- 1) Laplace...

Hi everybody. I need to take a course this spring called "intro to partial differential equations, Fourier series, and boundary value problems", and I'm wondering, how much vector calculus (if any) should I learn before this course starts? I have multivariable calculus and ODEs down just fine...

Homework Statement Solve the following PDE's: \frac{\partial u }{\partial t }+c \frac{\partial u }{\partial x} with u(x,0)=h(x). (1) \frac{\partial u }{\partial t }+u \frac{\partial u }{\partial x} with u(x,0)=h(x). (2) Hints: Specify the characteristic field of directions associated to each...

I have a system of non-linear coupled PDEs, taken from a paper from the 1980s which I would like to numerically solve. I would prefer not to use a numerical Package like MatLab or Mathematica, though I will if I need to. I would like to know if anyone knows how to solve non-linear coupled...

I made a small program to simulate the time development of a 1D wavepacket obeying the Schrodinger equation, mostly in order to learn a new programming language - so in order to not have to invoke big numerical methods packages, I opted for the simplest solution: The standard three-point...

Hey everyone, I'm taking intro ODEs right now, and am taking intro PDEs next semester. I would like to know what i should review from calc III for this course. I took calc III over the summer at a community college and didn't learn very much, if I'm being honest with myself. I think I am...

Hi, I was reading a paper on control of the 1-D heat equation with boundary control, the equation being \frac{\partial u(x,t)}{\partial x}= \frac{\partial^2 u(x,t)}{\partial x^2} with boundary conditions: u(0,t)=0 and u_x(1,t)=w(t), where w(t) is the control input. The authors...

Let us consider the following partial differential equation: {(}\frac{\partial z}{\partial x}{)}^2{+}{(}\frac{\partial z}{\partial y}{)}^{2}{=}{1} ---------- (1) The general solution[you will find in the texts: http://eqworld.ipmnet.ru/en/solutions/fpde/fpde3201.pdf is given by...

Hi, I have completed an undergrad introductory PDEs course using the Strauss text and am now transitioning to graduate PDEs using the Evans text. Though the first parts of these texts treat (generally) the same subjects, there is a vast gap between them in terms of 'mathematical maturity.'...

Hello, I have a PDE: 3*u_x + 2*u_y = 0, and I am interested in determining initial values such that there is a unique solution, there are multiple solutions, and there are no solutions at all. What theorem(s)/techniques would be of use to me for something like this? Regards, Dan

The code can be seen here: http://www4.ncsu.edu/~zhilin/TEACHING/MA584/MATLAB/ADI/adi.m If you can refere me to a book, paper, equation I would appreciate it, I have been following The Finite Difference Method in PDE from Mitchell but the methods briefly outlined there don't consider the...

Title says it all :smile:

i basically don't know how to do pde's, so I'm learning it from scratch today for my test which is tomorrow (which is in 24hrs from now, for those who don't live in australia), and notes/the internet arent nearly as good as explaining things as people are. so how would i go by starting these...

Hello: I am looking to solve a set of 1D PDEs. I thought the finite difference method would be a good way to go about it. So I decided to pick a simple first order forward difference scheme to obtain preliminary results. I just have 1 question: According to my scheme, at the last node...

I have the following system of first order PDEs \begin{array}{rcl} \frac{\partial v}{\partial t}+v\frac{\partial v}{\partial x} & = & -\varepsilon\gamma^{-3}(v)E \\ \frac{\partial n}{\partial t}+\frac{\partial}{\partial x}(nv) & = & 0 \\ \frac{\partial E}{\partial t}+E & = & nv \end{array}...

What kind of systems do ODEs describe? What kind of systems do PDEs describe?

I have an unusual question, though hopefully someone here can answer it. Apologies if this belongs in the homework forums, not really sure where to put it, as I'm not asking for help with the problems here. I'm currently in the second half of a 12-week third-year University course on PDEs. I...

See attached image for the question and my working. Hopefully you can read it OK, I had to resize it to fit to the allowed dimensions. I'm unsure how to proceed or if I have done something wrong previously - the initial and boundary conditions are tripping me up. The boundary conditions in red...

I've taken a first semester course on PDEs. Basically all we learned was separation of variables and method of characteristics. I understand that there are transforms out there, such as laplace and fourier. However, it looks like there aren't many analytical ways of solving PDEs. Mind you, I'm...

Homework Statement Hello, I'm having a problem solving second order inhomogeneous PDEs, for example the standard heat equation with a forcing term Sin(x)Sin(t) added onto it on the right hand side. Homework Equations ut = uxx + Sin(ax)Sin(bt) The Attempt at a Solution I can solve...

a question on orthogonality relating to Fourier analysis and also solutions of PDEs by separation of variables. I've used the fact that the following expression (I chose sine, also cosine works): \int_{0}^{2\pi}\sin mx\sin nxdx equals 0 unless m=n in which case it equals pi in...

Just quick question about sep of variables.. say have function U(x,y)=X(x)Y(y) when do separation of variables end up with some generic case that looks like: X''/X=Y'/Y=lamda my question is (and I think I know now the answer but would like confirmation), is what sign should the lamda...

Solving PDEs using Fouries Series ? Hello I am trying to solve 2D Laplace's equation (\nabla2u) using Fourier series using these boundary conditions for a square domain of length L: u(x, 0) = 0 u(0, y) = 0 u(L, y) = 0 u(x,L) = Uo After solving the 2 ODEs(separating variables method)...

Are PDEs or ODEs more useful? Especially in biochemistry/molecular biology. Would learning PDEs also allow one to deal with ODEs?