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# Questions tagged [finite-difference]

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

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### Initial Condition in a Numerical Problem

In a initial value problem does the initial condition has to satisfy the boundary condition and the governing equation? For example: If a non-homogeneous Neumann boundary condition for the pressure ...
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### Time discretization: Runge-Kutta methods vs. standard backward difference

I've recently written a code that solves the incompressible/low-Mach number formulation of the Navier-Stokes equation with high-order methods for both time and space. My advisor insisted that I use ...
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### Iteratively solving 3D Poisson equation in MATLAB

I have written a function that sets up a sparse matrix A and RHS b for the 3D Poisson equation in a relatively efficient way. The set-up is nothing fancy: I have extended the 2D 5-point stencil to an ...
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### 1-D incompressible unsteady Couette Flow Explicit finite differece CFD

I am currently following J.Anderson Jr.'s CFD with basic application and I came into some troubles while coding for my very first CFD problem. As the title suggests I am solving an incompressible ...
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### Numerically find Greens function

I am trying to numerically evaluate a Greens function for this equation: $$\left[\frac{\partial^2}{\partial x^2} + f(x) \right] G(x) = \delta (x-x_0)$$ With Neumann boundary conditions. Here, the ...
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### Mass conservation in atmospheric continuity equation numerical solution

My phd project is heavily related to numerical modeling of planetary atmospheres. In particular now I am dealing with a particular expression of the continuity equation, involving a thermodynamic flux....
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### Jacobi iteration for finite difference: when to stop?

I implemented a finite difference scheme to solve Poisson's equation in a 2D grid in C. I solve the system by using Jacobi iteration. Everything works fine until I use a while loop to check whether it ...
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### Runge-Kutta Stability Regions

Based on this link, in particular Figure 1, what is the exact meaning of the plot? To my understanding, it implies that for a given differential equation: $$\frac {dy}{dt} = \lambda y$$ that the ...
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### Methods to approximate discretized derivatives in PDEs

When solving a general PDE such as $$\frac {\partial ^2 E}{\partial t ^2} = \frac {\partial ^2 E}{\partial z ^2} - \frac {\partial E}{\partial z}$$ this equation can be solved by the method of ...
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