# Questions tagged [accuracy]

For questions about characterizing or improving the accuracy of a computational method.

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### Computing accuracy of my finite difference scheme for uniform grid on a non-uniform grid

I have a ADI finite difference scheme for the 2D Navier-Stokes equations that uses a second order accurate (central) approximation for the advective terms. I am ignoring the diffusive terms for now. I ...
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### Compute accuracy order as mesh gets refined?

I have implemented a FVM code and now I need to plot the accuracy of the method as the mesh gets refined. Having a very fine mesh, my idea is to compare what is the error between the coarser and fine ...
• 1,019
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### Finite differences vs. elements: Accuracy and implementation

I am trying to solve the 2D Poisson equation numerically: $\frac{\partial ^2 \phi}{\partial x^2} + \frac{\partial ^2 \phi}{\partial y^2} = 1$ with the Dirichlet boundary condition $\phi = 0$. I ...
• 41
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### boundary conditions with non-constant coefficients in cell centred finite volume method

Suppose am solving the heat conduction equation in 1d with Dirichlet boundary conditions. The thermal conductivity $k$ is a non constant function. So $-(k(x)u'(x))' = f(x)$ The value of $k$ enters the ...
• 435
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### Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy

I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states: $$(A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1}$$ I wish to perform small ...
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### Order of convergence of Scrodinger eq. with CN scheme

I'm trying to solve numerically the 1-dim time dependent Schrodinger equation using the Crank Nicolson scheme and the Thomas algorithm to solve the tridiagonal matrix. The physical system consists of ...
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### Known Algorithm to compute errors of given nature

I have three sets of data, measured by three different devices: A,B and C of air balloon whose fall is influenced by wind and ...
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### How to accurately decompose positive semidefinite matrix and use the lower triangular part in linear equations

I have $n$ arbitrary $p\times 1$ vectors $x_i$, and $p\times k$ matrices $A_i$, and $n$ $p \times p$ positive semidefinite matrices $S_i$, where some (often most) of the $S_i$'s are same (for example ...
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### Are there Improved ways of computing $p \log(p)$?

Most math libraries have a number of versions of logarithm functions. Most of the time we assume them to be perfect, but actually quite a lot of them just offer a certain number of digits of precision....
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