We carry out a systematic numerical stability analysis of ZND detonations of Majda’s model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat release and activation energy are varied. Our purpose is, first, to answer a question of Majda whether oscillatory instabilities can occur for high activation energies as in the full reacting Euler equations, and, second,...

Vector fitting is widely accepted as a robust macromodelling tool for efficient frequency domain identification of passive components. The orthonormal vector fitting technique is introduced, which improves the numerical stability of the method, by using orthonormal rational functions. This leads to better conditioned equations, reduces the numerical sensitivity to the choice of starting poles s...

Abstract The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better unde...

This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually imp...

Non-standard backward heat conduction problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result shows that our algorithm is effe...

An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S2 in R3 of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S2 (known as...

B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight into modified differential equations of backward error analysis. These two laws give rise to algebraic structures (groups and Hopf algebras of...

Earlier work by Driscoll and Healy [4] has produced an efficient O(B log B) algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper, we discuss an implementation of an O(B) algorithm for the numerical computation of Fourier transforms of functions defined on the rotation group, SO(3). This compares with the direct O(B) approach. The algorithm we im...

Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opin...

This paper is concerned with the numerical solution of implicit neutral functional diierential equations. Based on the continuous Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equations), two general one-step methods are formulated and their uniform order of approximation are discussed. Numerical stability of a class of Runge{Kutta-Collocatio...