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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3
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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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votes
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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 ...
- 1,320
5
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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 ...
- 151
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1
answer
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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....
10
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4
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Fast and accurate double precision implementation of incomplete gamma function
What is the state of the art way of implementing double precision special functions? I need the following integral:
$$
F_m(t) = \int_0^1 u^{2m} e^{-tu^2} d u
= {\gamma(m+{1\over 2}, t)\...
- 2,920
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Demonstrating that the time step size is small enough in a code with automatic step size selection
I recently inherited a large body of legacy code that solves a very stiff, transient problem. I would like to demonstrate that the spatial and temporal step sizes are small enough that the ...
- 4,587
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How do you improve the accuracy of a finite difference method for finding the eigensystem of a singular linear ODE
I am attempting to solve an equation of the type:
$ \left( -\tfrac{\partial^2}{\partial x^2} - f\left(x\right) \right) \psi(x) = \lambda \psi(x) $
Where $f(x)$ has a simple pole at $0$, for the ...
- 1,155
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Are 8 Gauss points required for second order hexahedral finite elements?
Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical ...
- 3,889
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Is there software that can autogenerate numerically-accurate floating point C routines from symbolic formulae?
Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE ...
- 353
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numerical integration with possible division by 'zero'
I am trying to integrate
$$\int^1_0 t^{2n+2}\exp\left({\frac{\alpha r_0}{t}}\right)dt$$
which is a simple transformation of
$$\int^{\infty}_1 x^{2n}\exp(-\alpha r_0 x)dx$$
using $t = \frac1{x}$ ...
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When is a high order method useful for computational fluid dynamics simulations?
Many numerical approaches to CFD can be extended to arbitrarily high order (for instance, discontinuous Galerkin methods, WENO methods, spectral differencing, etc.). How should I choose an ...
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