Accuracy and stability of numerical algorithms

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For solving the dynamic equilibrium equation of structures, several second-order numerical methods have so far been proposed. In these algorithms, conditional stability, period elongation, amplitude error, appearance of spurious frequencies and dependency of the algorithms to the time steps are the crucial problems. Among the numerical methods, Newmark average acceleration algorithm, regardl...

P-stability‎, ‎TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...

The effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows by Lattice-Boltzmann method

The aim of this study is to investigate the effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows in the context of single relaxation time Lattice Boltzmann method (SRT-LBM). The fluid flows are simulated using regularized, no-slip, Zou-He and bounce back boundary conditions for straight surfaces in a lid driven cavity and the two-dimensional flow ...

Umist Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra Departments of Mathematics Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra 1

Camparison of Numerically Stability of Two Algorithms for the Calculation of Variance

In descriptive statistics, there are two computational algorithms for determining the variance S2, of a set of observations : Algorithm 1: S2= - , Algorithm 2: S2= , where . It is interesting to discuss, which of the above formulas is numerically more trustworthy in machine numbers sets. I this paper, based on total effect of rounding error, we prove that the second Algorithm is better...

Symplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...