1
vote
0answers
30 views

stability of FTCS scheme for parabolic equation

Can you suggest any method for stability analysis of FTCS scheme for the the following parabolic equation ? D.E: $u_{t}=a(x,t)u_{xx}+f(x,t,u)$, $0<x<1$, $0<t<T$, $T>0$ BCs: ...
0
votes
0answers
17 views

Finite difference method for elliptic pde stability condition

I am trying to implement a finite difference scheme for the elliptic pde $\nabla(a(x_1,x_2)\nabla\phi(x_1,x_2))=0$ where $(x_1,x_2) \in (0,l_1)\times(0,l_2)$ with $l_1 \neq l_2$ necessarily. I know ...
2
votes
1answer
65 views

Numerical methods for inverting non positive definite matrices

I'm working on a PDE solver and need to invert the following matrix written in block form $\left( \begin{array}{cc} kM & -S \\ -S & M \end{array}\right) $ where M and S are the usual mass and ...
4
votes
1answer
439 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, ...