Questions tagged [accuracy]

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437 views

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 ...
536 views

Order of accuracy of FVM discretization

I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :) ...
79 views

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 ...
140 views

Derivative of Whittaker-Shannon interpolant

Last time we looked at how to improve the accuracy of Whittaker-Shannon interpolation, where user njuffa demonstrated that judicious use of sin_pi could greatly ...
107 views

How can I evaluate the accuracy of my n-body simulation?

I am making an n-body simulation in python. There are many different methods to numerically solve the system of differential equations governing the gravitational interactions between the $n$ ...
212 views

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 ...
173 views

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 ...
49 views

Quick evaluation of floating point Absolute Error

I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok. The ...
183 views

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 ...
45 views

Comparison between stability and accuracy of various Finite Difference schemes

I`m Analyzing the 1D convection equation (PDE) for stability, consistency, and accuracy. I know Both upwind schemes (explicit and implicit) show better stability with a higher number of waves for ...