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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 ...
Verlet integration (French pronunciation:) is a numerical method used to integrate Newton's equations of motion. [1] It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics .
Improved versions of MPS method have been proposed for enhancement of numerical stability (e.g. Koshizuka et al., 1998; Zhang et al., 2005; Ataie-Ashtiani and Farhadi, 2006;Shakibaeina and Jin, 2009; Jandaghian and Shakibaeinia, 2020; Cheng et al. 2021), momentum conservation (e.g. Hamiltonian MPS by Suzuki et al., 2007; Corrected MPS by Khayyer and Gotoh, 2008; Enhanced MPS by Jandaghian and ...
The stability region of the semi-implicit method was presented by Niiranen [5] although the semi-implicit Euler was misleadingly called symmetric Euler in his paper. The semi-implicit method models the simulated system correctly if the complex roots of the characteristic equation are within the circle shown below.
In the area of mathematics known as numerical ordinary differential equations, the direct multiple shooting method is a numerical method for the solution of boundary value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem in each of the smaller intervals ...
In numerical linear algebra, the biconjugate gradient stabilized method, often abbreviated as BiCGSTAB, is an iterative method developed by H. A. van der Vorst for the numerical solution of nonsymmetric linear systems.