This article reviews linear instability analysis of flows over or through complex two-
dimensional (2D) and 3D geometries. In the three decades since it first appeared in the …

This article presents a fairly up to date survey of the research literature relating to differential-
algebraic equations (DA Es) and their numerical solution In contrast to ordinary differential …

The development of ARPACK began as a research code written in Matlab and then in
Fortran 77 in 1990. Initially, the code was developed to study and verify the properties of the …

In many large scale scientific or engineering computations, ranging from computing the
frequency response of a circuit to the earthquake response of a buildingto the energy levels …

This book describes numerical methods for the detection, computation, and continuation
(following paths) of equilibria and bifurcation points of equilibria of dynamical systems. In the …

We provide an overview of current techniques and typical applications of numerical
bifurcation analysis in fluid dynamical problems. Many of these problems are characterized …

This document describes slePc, the Scalable Library for Eigenvalue Problem Computations,
a software package for the solution of large sparse eigenproblems on parallel computers. It …

In this review we discuss bifurcation theory in a Banach space setting using the singularity
theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical …

Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing
Reynolds numbers Page 1 J. Fluid Mech. (2022), vol. 940, A11, doi:10.1017/jfm.2022.222 …

Knowledge of the rightmost eigenvalues of system matrices is essential in power system
small-signal stability analysis. Accurate and efficient computation of the rightmost …