# pde

1. ### Finite Differences: Which of the following schemes numerically approximates the solution?

I've got the following PDE: $u_{tt}(x,t) = \pi u_{xx}(x,t) \quad x \in [0,1], t > 0 \\ u(x,0) = 18sin(3\pi x) \quad \forall x \in [0,1]\\ u_{t}(x,0) = sin(\pi x) \quad \forall x \in [0,1]\\ u(0,t) = u(1,t)=0 \quad \forall t > 0$ Which of the following schemes can numerically...
2. ### Hard PDE

Solve \frac{\partial Z }{\partial x} =2x\cdot (1-\frac{\partial Z}{\partial y})\; , for Z(x,0)=Z(0,y)=1 .
3. ### PDE solution explanation

Given equation : zâ€™_{x} a(x) +zâ€™_{y} b(y)=c . Why the solution is found by dx/a(x)=dy/b(x)= c/dz ?
4. ### Euler's equation and PDE

I am unable to solve the PDE attached using Euler's concept. The answer I am getting is not matching with the one given. Please help me deduce the answer.
5. ### 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...
6. ### Transformation of Equations - What is the deeper thing?

Hi, If you have an ordinary differential equation (or equations), you can transform them under some conditions (integral, linear operator, ...) to algebraic equations. If you have a partial differential equation you may transform it to an ODE. This can be shown "easily" by doing Fourier...
7. ### A PDE solution

Let $f\in C^2(\mathbb{R}^n)$. We define $$\phi(x,r)=\frac{1}{n\alpha(n)}\int_{\partial B(0,1)}f(x+rz)dS(z)$$ where $\alpha(n)$ is the volume of $B(0,1)$. I calculated $$\partial_r\phi=\frac{r}{n\alpha(n)} \int_{\partial B(0,1)}\Delta_xf(x+rz)dS(z)$$ Please help me to show that...
8. ### solving heat PDE using FFCT

solving heat PDE using FFCT the problem is solve the following heat problem using FFCT: A metal bar of length L, is at constant temperature of $U_0$ , at $t=0$ the end $x=L$ is suddenly given the constant temperature of $U_1$ and the end x=0 is insulated. Assuming that the surface of the bar...
9. ### solving heat PDE using FFCT

the problem is solve the following heat problem using FFCT: A metal bar of length L, is at constant temperature of $U_0$ , at $t=0$ the end $x=L$ is suddenly given the constant temperature of $U_1$ and the end x=0 is insulated. Assuming that the surface of the bar is insulated, find the...
10. ### Prove PDE of a Brownian motion by direct differentiation

Any help in the question below will be highly appreciated.
11. ### Prove PDE of a Brownian motion by direct differentiation

Could anyone assist me with the question attached?

Attached
13. ### PDE for a brownian motion

1. By direct differentiation, prove the partial differential equation of he Brownian motion with a mean of y âˆ’ a(T âˆ’ t) and variance b(T âˆ’ t). 2. By direct differentiation, prove the the partial differential equation of the Brownian motion with a mean of y and variance b(T âˆ’ t)...
14. ### Solving for PDE Eigenvalues

Eigenvalue PDE? How can I solve for lambda of the new problem exactly how the old problem was solved. Both problems are included in the attached picture. Please show steps
15. ### solving a multi-dimensional non-homogeneous transient PDE

Hi, in the context of my graduation project I want to solve a 2D, transient hon-homogeneous conduction problem with convective boundary conditions in cylindrical coordinates (see file attached ) according to an online source: "This problem can be decomposed into a set of steady state...
16. ### How can I solve this PDE?

-(âˆ‚Â²u/âˆ‚xÂ² + âˆ‚Â²u/âˆ‚yÂ²) + ukÂ² = xkÂ² zero boundary conditions on the boundary of the Square Domain (0,1)X(0,1). k^2 is a constant
17. ### pde

I need a hint for this exercise!
18. ### Second Order PDE missing component?

So I got this exercise where I'm suppose to solve Z using variable change. I'v written it rather clean so here's a picture of my attempt at a solution. As you can see I end up with 0 = x/y^2 I can only assume what I miss is a another Z''xy component or something but I dont see what I'v...
19. ### Whether to define system as PDE or ODE

Hey everyone. I'm a grad student revising a journal article. Within the article, I layout an equation which describes of population "n(r)" through time. The parameters of this population vary with some variable "r"; however, r does not change with time. When I solve this system (written out...
20. ### Solve PDE - elliptic equation

Hi, I have to solve this PDE: $U_{xx} +U_ {xy}+U_{yy}+sin(u)=12*(x^2+y^2)+sin(x^2+y^2)$ The domain is $U(0, y)=y^4; U(1, y)=1+y^4; U(x, 0)=x^4; U(x, 1)=1+x^4;$ First of all I think that I change the equations in canonical form, I do this with: \$ { ( eta=((3)^(1/2)x/2 ),(...