# Questions tagged [finite-difference]

Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.

855 questions
Filter by
Sorted by
Tagged with
180 views

### Finite difference problem

I have a problem to resolve with the Finite Difference method in $[a,b]$: $$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$ with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
45 views

### Is a sort of "z-drift" the result of numerical precision errors in FDM?

Upon solving the 2D wave equation with Neumann boundary conditions $u_x = u_y = 0$ on a rectangular $10 \times 10 \times 10$ grid, I noticed something odd - $u$ seemed to shift upwards with time. This ...
175 views

### Stability of Euler forward method

I am trying to solve a linear system of ODEs of the form: $$\frac{du}{dt} = A u, \quad u(0)=k$$ where $A$ is a 2x2 matrix and $u(t)$ is a 2x1 column vector. I want to solve this numerically, using ...
1 vote
82 views

### derivative matrix and the Dirac delta distribution

For a project I'm working on, I was working with the following equation $$w(x) = \int k(x,y)v(y)dy$$ I noticed that if I choose $$k(x,y) = -\delta'(x-y)$$ Then we probably get (I haven't touched ...
1 vote
72 views

### Does anyone know how to add a forcing term at the center of a cicular membrane?

I am here once again searching for wisdom, as some of you might notice I asked a related question a few days ago. And now I am struggling to add a forcing term at the center of the membrane, in order ...
97 views

129 views

1 vote
61 views

### Once Lyapunov exponents have converged, can they diverge again?

I know the strength of attraction for a single attractor might vary from place to place. Say, if I calculated the Lyapunov exponents for a small portion of the attractor and they have already ...
112 views

### How to numerically solve differential equations involving sines, cosines and inverses of the unknown function?

I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method. I find that the main idea is to ...
1 vote
226 views

### Partial derivatives for triangular meshes (in 3D)

A grid offers an obvious definition for the partial derivatives at a grid point, given $x$ the value of a point $p$ in an $n$ dimensional grid, the forward partial derivative that point for coordinate ...
39 views

### Refluxing step on Finite difference AMR

Hi I am a computer scientist working on MHD code for astrophysics simulation. We use a finite difference scheme where we first solve the spatial derivatives and with them solve the right hand side and ...
74 views

305 views

1 vote