Showing papers in "Applied Mathematics and Computation in 1987"

TL;DR: A new method for defining a homotophy to find all solutions to a polynomial system, F(z) = 0, of n equations in n unknowns using a generic homotopy, which represents a significant advance over previous homotopies.

TL;DR: This paper establishes some principles of implementation and reports on the performance of programs that use the new homotopies, which are faster and more reliable than previous approaches.

TL;DR: The problem can be solved by a unified approach, quickly and reliably, when many systems with the same structure must be solved quickly, as in finite-difference models of fluid flow and combustion.

TL;DR: In this paper, the first and second partial derivatives of the Perron root of a positive reciprocal matrix are derived and used in conjunction with Saaty's analytic hierarchy process, a decision-analysis method which is based upon pairwise comparisons among a set of alternatives over various criteria.

TL;DR: In this article, the authors established the uniform convergence and obtained convergence rates for several algorithms for solving a class of Hadamard singular integral equations, and improved on the mean square convergence shown in [2].

TL;DR: In this paper, a review of the use of equidistribution of a weight function over a mesh is presented, and the shortcomings of this approach are identified, and its usefulness is evaluated.

TL;DR: The Chow-Yorke algorithm is a homotopy method that has been proved globally convergent for Brouwer fixed-point problems, certain classes of zero finding and nonlinear programming problems, and two-point boundary-value approximations based on shooting and finite differences as discussed by the authors.

TL;DR: In this article, a method for numerically solving linear singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the underlying interval is proposed.

TL;DR: In this paper, finite element approximation schemes for boundary value problems for linear first order elliptic systems in three dimensions were considered. And a least square method and a new subdomain-collocation-least-squares method were considered, yielding optimal asymptotic H 1 ε and L 2 ε error estimates.

TL;DR: In this article, a two-level iterative method for 3D elasticity problems discretized by quadratic elements is proposed, where the coarse level consists of linear elements.

TL;DR: In this article, a study has been conducted to investigate the adaptive grid method, based on the concept of equidistribution, applied to Navier-Stokes flow computations, and it is shown that due to the fundamental differences between the structure of the pressure field and the velocity field, an adaptive grid strategy that employs multiple one-dimensional grid adjustment procedures using different weighting functions for different directions is useful.

TL;DR: In this paper, the authors present certain new results from discrete relative dynamics in bifurcation theory in two-and three-location, one-stock interactive dynamics, including the following: (i) the discrete-relative-dynamics analogue to the Hopf bifurbation of the continuous-Dynamics case; (ii) the demonstration of "local, partial turbulence" in discrete relative dynamic dynamics; (iii) the presence of "strange containers'' equivalent to these labeled ''strange attractors'' in the current literature on continuous (fixed-

TL;DR: A method is presented for automatically computing the exact value of the gradient of equations of many variables using much less than 64 kb of memory and only a small amount of computer time.

TL;DR: In this paper, a new approach to numerically solving linear, singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the interval is presented.

TL;DR: In this article, a control system consisting of a linear control to stabilize the nominal system, a nonlinear control to cope with the uncertainties, and an insensitive observer for the state estimation is presented.

TL;DR: In this article, an approximate method for the numerical solution of linear singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the underlying interval is presented.

TL;DR: In this paper, closed form expressions for the probability densities of the parameters that control the characteristics of the dynamic response of a structure modeled by a single-degree-of-freedom system in which the mass, stiffness, and damping parameters are only imprecisely known.

TL;DR: In this paper, a general approach to the development of deterministic equivalents of constraints to be satisfied within certain probability limits is presented, and a deterministic transformation of a stochastic programming problem with random variables in the objective function is presented.

TL;DR: A unidirectional optimal search algorithm is substituted for the set of fixed rules usually employed to modify the simplex, which proves especially effective in dealing with ''narrow valley'' situations, normally encountered whenever the decision variables exhibit some degree of correlation.

TL;DR: In this paper, various properties of nonlinear difference equations are analyzed within the framework of a model of endogenous preference change, focusing on the sequence of stable cycles and questions about rationality and consistent behavior over time within a structure of utility maximization.

TL;DR: In this article, the behavior of nonlinear dispersive or dissipative waves is analyzed using the decomposition method, and the authors propose a decomposition-based approach to analyze the dispersive and dissipative wave behavior.

TL;DR: This paper presents a finite algorithm for computing the weighted Moore-Penrose inverse of a rectangular matrix that may be viewed as an extension of Decell's algorithm.

TL;DR: In this paper, the authors examined the effect of increasing the number of lines used in the MOL representation of the original PDE and showed that the instability usually blamed on MOL has its origin in the original equation.

TL;DR: In this article, an analytical comparison of the various elliptic partial-differential-equation (PDE) models which are in current use for grid generation is devoted to the transverse coordinate leaving the surface is orthogonal to the surface.

TL;DR: In this article, an interactive approach for solving a multiple objective linear programming (MOLP) problem is presented, which assumes that the decision maker (in contrast to the analyst) can establish a (preferential) partial order P"v on the decision variables and a partial order p"o on the objective functions.

TL;DR: An adaptive method based on the trapezoidal rule for the numerical solution of Fredholm integral equations of the second kind is developed in this paper, where the choice of mesh points is made automatically so as to equidistribute both the change in the discrete solution and its gradient.

TL;DR: In this article, an interesting variation of the author's decomposition method, first proposed in 1983, which permits determination of the behavior of the solution of a differential equation as the independent variable approaches infinity, is considered.

TL;DR: In this article, a nonlinear variation of parameter method of Bernfeld and Lord for systems of ordinary integrodifferential and integral equations is corrected and extended, and representation formulas for certain solutions of perturbations of such systems are obtained.

TL;DR: In this paper, the authors show how the sums of Chebyshev and Legendre series can be approximated as accurately as we please in many cases, without explicit knowledge of f(u).

TL;DR: In this article, the authors considered the existence of solutions of initial and periodic value problems of first order differential equations and combined the method of upper and lower solutions and lower solution and the interval method.