# pde

1. ### Partial Derivative Equation as solutions

I have to solve PDE as ODE, but my lecturer didn't give me enough help and tutorial, to solve these problems. I searched YouTube and other websites to find a clue how to solve them but I find no clue. Please help! The problems are: i have to solve PDE as ODE where u = u(x,y) u_y + u = e^{xy}...
2. ### Partial Differential Equation

Help please, I need to solve this differential equation x\frac{\partial^2 U}{\partial x^2}+y\frac{\partial^2 U}{\partial y^2}=aU in Matlab (where "a" is a constant parameter, it can be taken by any), I wanted to use the Partial Differential Equation Toolbox, but I ran into a problem, the...
3. ### Linear PDE struggling to find a solution

Im struggling with the following problem My problem comes on trying to integrate on the simultaneous ODE system. = 0
4. ### How to write Matlab code for this PDE problem?

Hello, so I have this problem and I did not receive full credit on it and I would love to have the correct answer for future problems. I attached an image of the problem and what I had and I could never get my code to run so any help is appreciated. Thanks! dx = 1e-2; dt = 1e-5; u(x,0) =...

6. ### Partial Differential Equation numerical problem

Im working on the following PDE problem: I have found an analytical solution and also computed a numerical solution using the forward difference scheme. I chose the largest time value equal to 1 and from the stability condtion dt/dx^2 =< 1/2, when choosing the x - step dx = 1/10 where x(n) =...
7. ### Investigating a Parabolic PDE algorithm (Urgent please)

Hi - this is my 2nd post today, the assignment is due tomorrow (I should have thought of using this forum earlier), I just have two exercises partly finished and being a bit of a perfectionist I would prefer to have them completed, appreciate all help. I am given a very basic fortran program...
8. ### Discretising Elliptic PDE in cylindrical coordinates (Urgent)

Hi - I've been battling with this for weeks and the assignment is due tomorrow, I should have tried this forum earlier I know. Below is as far as I can get, I think I'm missing a crucial piece of knowledge. We are given an energy functional using cylindrical coords:  E=\int_{0}^{\infty}...

10. ### Analytical Solution to 1D Heat Equation with Neumann and Robin Boundary Conditions

Hello, I'm modeling the 1D temperature response of an object with an insulated and convection boundary conditions. Consequently, I'm looking for the solution for the 1D heat equation with neumann and robin boundary conditions, but I can't seem to get a hold of it, despite my arduous search. I'm...
11. ### 2nd oder PDE, wave equation

Solve, ut=uxxc2 given the following boundary and initial conditions u(0,t)=1,u(L,t)=3 u(x,0)=f(x),ut(x,0)=g(x) How do I being to solve this since, u(0,t) and u(L,t) does not equal 0?
12. ### Finite difference method nonlinear PDE Problem

i want to solve a nonlinear PDE with finite difference method , from my academic background , i know how to use finite difference method to solve linear PDE , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me...
13. ### Second order PDE

ut = uxx - 2u boundary conditions: u(0,t) = 0, u(1,t) = 0 initial condition: u(x,0) = sin(pi*x) - sin(4*pi*x) I am having trouble understanding why if you let the PDE becomes Can someone clarify to me how this works?
14. ### Converting a simple PDE into an ODE for solving

Hey guys. A have a very simple PDE (along with an initial condition and a boundary condition) which I wish to turn into an ODE so I can solve. Even though the PDE seems very simple, I haven't been able to find any examples on it so I'm actually quite stumped. The PDE is: -a*(dy/dx) = (dy/dt)...
15. ### Fourier transform of PDE

Hi I have the following PDE \frac{\partial f}{\partial t}=-A\frac{\partial f^4}{\partial x^4}+B\frac{\partial f^2}{\partial t^2} Show if Fourier transform satisfies (which I have, using FT of derivatives) \frac{\partial \tilde{f}}{\partial t}(k,t)=-(Ak^4+Bk^2)\tilde{f}(k,t) Then the PDE for...
16. ### Classifying second order PDE

When classifying PDEs as elliptical, parabolic or hyperbolic, would the B term when finding the discriminant be B=B1+B2? A\frac{\partial^2 u}{\partial x^2}+B_{1}\frac{\partial^2 u}{\partial x\partial y}+B_{2}\frac{\partial^2 u }{\partial y\partial x}+C\frac{\partial^2 u}{\partial y^2}+...
17. ### solve the PDE

Hey guys, I'm having trouble solving for the term in the second order PDE. My problem is that I cannot solve for some of the term In this question, I let X(x) to be equal to Asin(kx)+Bcos(kx) (since I have seen X(x) being equal to this before) The problem is, I do not know how/why did X(x)...