0
votes
0answers
21 views

Final value problem PDE

I need help unterstanding and solving the following problem $\rho c_p \frac{\partial\lambda}{\partial t} + k \frac{\partial^2\lambda}{\partial x^2} + 2 [T(x,t,q(t)) - Y(t)] \delta(x-x_{s}) = 0 $ ...
2
votes
1answer
92 views

Matlab help related with discretization of second order elliptic partial differential equation

I am reading this paper. In Example 2 from this paper, linear system of equation $Ax = b$ is given, where coefficient matrix $A$ has been generated by he five-point discretization of the following ...
0
votes
2answers
112 views

Laplace equation in 1D with MATLAB - Neumann boundary condition

My previous problem is here and I 've done. Laplace equation in 1D with MATLAB I have the next problem: solve Laplace equation in $1$D with boundary condition $u'(0)=u'(1)=0$ Help me some hints. ...
1
vote
1answer
50 views

Is there something useful for third boundary condition on Poisson equation

There is a following task for a friend of mine to make: $$-\Delta u=f,x\in(0,X),y\in(0,Y)\\-u_x+\alpha(y)u\Bigr|_{x=0}=g(y)\\u\Bigr|_{x=X}=c(y)\\u\Bigr|_{y=0}=a(x)\\u\Bigr|_{y=Y}=b(x)$$ She needs ...
0
votes
0answers
81 views

Stuck on a hideous partial differential equation

I'm stuck on this PDE: $$\rho \cdot C \cdot \dfrac{\partial T}{\partial \tau} + u \cdot \rho \cdot C \cdot \dfrac{\partial T}{\partial r} = \dfrac{\lambda}{r^{2}} \cdot \dfrac{\partial}{\partial ...
1
vote
1answer
434 views

Solving Laplace's equation using finite differences

I having coding in MatLab to approximate solutions to Laplace's equation in 2D using finite differences. I was able to do it without much problem. I learnt about how to implement this using this: ...
0
votes
3answers
184 views

Numerical solution of system of PDEs (1 order,linear,homogenious) method Lax-Wendroff

I'm trying to solve linear system of PDEs $$\frac{\partial \bar{u}}{\partial t}+\begin{pmatrix} \frac{2}{5} & -\frac{72}{5} & \frac{64}{5} \\ \frac{6}{5} & \frac{-56}{5} & ...
3
votes
2answers
2k views

heat equation with Neumann B.C in matlab

$$ \frac{\partial u}{\partial t}=\alpha\frac{\partial^{2}u}{\partial x^{2}} \qquad u(x,0)=f(x)\qquad u_{x}(0,t)=0\qquad u_{x}(1,t)=2 $$ i'm trying to code the above heat equation with neumann b.c. ...
0
votes
0answers
71 views

How does one more Efficiently Numerically Solve Multidimensional Problems using Spectral Methods?

As per the title, would you please tell me how to more efficiently solve multidimensional partial differential equations? Other then just tediously writing out the matrix elements manually. If you ...
0
votes
1answer
2k views

solving pde by matlab

Can you help me please? I need to solve wave equation using Matlab. How to solve this PDE by Matlab? $u_{tt}=c^{2}u_{xx} $ for $0<x<l$ B.C: $u_x(0,t)=0$; $u(l,t)=0$ I.C: $u(x,0)=f(x); ...
3
votes
2answers
534 views

Inverse problem from pdes

A linear inverse problem is given by: $\ \mathbf{d}=\mathbf{A}\mathbf{m}+\mathbf{e}$ where d: observed data, A: theory operator, m: unknown model and e: error. To minimize the effect of the noise; ...
4
votes
1answer
343 views

How do I numerically calculate a function from its noisy gradient using “global integration”?

I have the model $\ s(x,y)=x^2+y^2, 0 \leq x \leq 1, 0 \leq y \leq 1 $. Instead of observing the model directly I am observing the derivatives of the model + some noise (e): $\ p(x,y)=s_x+e, ...
1
vote
1answer
378 views

Numerical solution of the Laplace equation on circular domain

I was solving Laplace equation in MATLAB numerically. However I have problems when the domain is not rectangular. The equation is as follows: $$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 ...
0
votes
1answer
251 views

Solving a system of equations that vary in time and space implicitly

I am writing a code for a system of equations for which the variables vary in time and space. I have written an implicit code to solve a system of equations before but in that case I could write the ...
0
votes
0answers
135 views

Matlab: Solving $u_t = f(u) u'' + g(u) u' + h(u) u$

I am trying to solve this equation (numerically) $$\dfrac{\partial u}{\partial t}=\dfrac 3 x\dfrac \partial{\partial x}\left(\sqrt x \frac \partial {\partial x}(\nu(u,u^2,\cdots,u^k)u\sqrt ...
2
votes
1answer
3k views

Can't understand a simple wave equation matlab code

I'm trying to figure out how to draw a wave equation progress in a 2D graph with Matlab. I found this piece of code which effectively draw a 2D wave placing a droplet in the middle of the graph (I ...