Search results
Results from the WOW.Com Content Network
Stability is sometimes achieved by including numerical diffusion. Numerical diffusion is a mathematical term which ensures that roundoff and other errors in the calculation get spread out and do not add up to cause the calculation to "blow up". Von Neumann stability analysis is a commonly used procedure for the stability analysis of finite ...
The stability of numerical schemes can be investigated by performing von Neumann stability analysis. For time-dependent problems, stability guarantees that the numerical method produces a bounded solution whenever the solution of the exact differential equation is bounded.
Numerical stability is the central criterion for judging the usefulness of implementing an algorithm on a computer with roundoff. For the Lanczos algorithm, it can be proved that with exact arithmetic , the set of vectors v 1 , v 2 , ⋯ , v m + 1 {\displaystyle v_{1},v_{2},\cdots ,v_{m+1}} constructs an orthonormal basis, and the eigenvalues ...
K. Shibata and S. Koshizuka, "Numerical analysis of shipping water impact on a deck using a particle method," Ocean Engineering, Vol 34, pp. 585–593, 2007. Y. Suzuki, S. Koshizuka, Y. Oka, "Hamiltonian moving-particle semi-implicit (HMPS) method for incompressible fluid flows," Computer Methods in Applied Mechanics and Engineering, Vol 196 ...
In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [ 1 ]
Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem.
It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical solution. As a consequence, the time step must be less than a certain upper bound, given a fixed spatial increment, in many explicit time-marching computer simulations ; otherwise, the simulation produces incorrect or unstable results.
The numerical stability is reduced compared to the naive algorithm, [6] but it is faster in cases where n > 100 or so [7] and appears in several libraries, such as BLAS. [8] Fast matrix multiplication algorithms cannot achieve component-wise stability, but some can be shown to exhibit norm-wise stability. [9]