# Questions tagged [finite-differences]

A method in numerical analysis which consists of approximating the derivatives of a solution of an ordinary or a partial differential equation. This leads to the solution of a linear system.

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### Final value of a recursion

Problem Given $p_1, \sigma > 0$, consider the following recursion \begin{equation*} p_{i}=(1-L_i)p_{i-1} \qquad i=2,\dots,k \end{equation*} where \begin{equation*} L_i \triangleq \frac{p_{i-1}}{p_{...
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### Numerical Analysis of Differential Equation with Boundary Conditions

Note I have decided to edit this post so it is more specific and also because I was incorrect the first time. I didn't wanna make another post about the same subject, but if this is not allowed then ...
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### implicite scheme for reaction diffusion equations under finite difference

I am trying to implement an implicit scheme for the following RD equation: $$u_t = \Delta u+f(v)u$$ where $v$ is a known data and $f$ is the reaction function. The initial is zero and non flux. To ...
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### How do I Helmholtz decompose a vector field on a two dimensional lattice if the curl and divergence of the said field is known? [closed]

I have a 2d vector field obtained from processing an image. I also have at my disposal the divergence D and curl C of this field. I want to Helmholtz decompose this field to obtain its rotational and ...
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### Numerical Partial Differential Equation

The solution of the difference diagram for some partial differential equations from the Fourier transform and Fourier analysis can be written in ${U_{n}}^{k}=q^{k}e^{in\xi}$ form. The condition for ...
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### The real CFL condition for cylindrical laplacian

I've been exploring the CFL (Courant-Friedrichs-Lewy) condition in polar coordinates and have observed that previous inquiries haven't yielded a satisfactory answer. I've come across this paper which ...
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### Transform Lagrangian with a square root

I have an action given by, $$S = \int^{\tau_f}_{\tau_0} d\tau \left(\frac{1}{z^3}\sqrt{-f(u,z) \dot{u}^2 + 2 \dot{u} \dot{z} + \dot{x}^2} + \frac{2 \dot{z}}{z^3} \right),$$ ...
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### Coupled non-linear PDE analytical solution to verify numerical solution.

as part of a computational module we were given the following coupled PDEs and solved them numerically using finite difference methods: I got the following graphs representing the numerical solution ...
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### Finite Difference Method for Poisson's Equation

I'm writing a Python program to solve Poisson's equation $$\nabla^2 u = f \quad \mathrm{on} \quad \Omega$$ with $$\frac{\partial u}{\partial n} = 0 \quad \mathrm{on} \quad \partial \Omega.$$ Here,...
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