0
votes
0answers
139 views

solving laplace in 3d using finite differences

I have created a function laplace3d() which accepts a 3D array describing the boundary conditions and -Inf at the places of unknown. It then calculates these ...
1
vote
1answer
92 views

Finite difference method stability

I have shown that a finite difference method satisfies $$\underline{u}^{n+1}=((1+6\mu)\mathbb{I}-36\mu A^{-1})\underline{u}^n$$ I don't think that the rest of the question is necessary but it is ...
2
votes
1answer
284 views

How do I solve an overdetermined linear system of partial differential equations?

I have two partial differential equations that I want to solve (for $\ \sigma $) by finite differences: $\ -\frac{\partial \sigma}{\partial x}(x,y,t) -p(x,y,t)\frac{\partial \sigma}{\partial t}(x,y,t) ...
0
votes
1answer
277 views

Solving Linear Systems with Singular Matrices

Good morning! For (say, homogenous) linear systems of the form $$x_{n+1} = A x_n,$$ where $A$ is a nonsingular matrix, each initial value problem can be solved by the method of finding a general ...