Journal ArticleDOI
Boundary Value Problems on Semi-Infinite Intervals and Their Numerical Solution
TLDR
In this paper, the problem of determining appropriate ABCs to use at a finite point was studied for both linear and non-linear boundary value problems, and a theory for doing this correctly was devised, which consists in determining appropriate asymptotic boundary conditions.Abstract:
To solve boundary value problems posed on semi-infinite intervals the problem is frequently replaced by one on a finite interval. We devise a theory for doing this correctly for both linear and nonlinear problems. In brief the method consists in determining appropriate asymptotic boundary conditions (ABC) to use at a finite point. In the linear case these are “projections” into the subspace of bounded solutions. In the nonlinear case, nonlinear boundary conditions result. They involve possibly unknown projections for the problem linearized about the solution at infinity. A linear eigenvalue problem for the Schrodinger equation and a nonlinear elasticity problem are solved to show the power of the new methods.read more
Citations
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Book
Sourcebook of parallel computing
Jack Dongarra,Ian Foster,Geoffrey C. Fox,William Gropp,Ken Kennedy,Linda Torczon,Andrew B. White +6 more
TL;DR: This chapter discusses parallelism in the context of scientific computing, which has applications in environment and energy, problem-Solving Environments, and more.
Journal ArticleDOI
The dependence of bacterial sulfate reduction on sulfate concentration in marine sediments
TL;DR: In this paper, the effect of dissolved sulfate concentration on the rate of bacterial sulfate reduction in marine sediment from Long Island Sound was examined using a radio-sulfur technique.
Journal ArticleDOI
Steady Viscous Flow Past a Circular Cylinder up to Reynolds Number 600
TL;DR: In this paper, it was found that the wake bubble grows in length approximately linearly with Re. The width increases like Re12 up to Re = 300 at which the wake resembles a pair of translating, uniform vortices, both touching the center line.
Book ChapterDOI
Lecture Notes on Numerical Analysis of Nonlinear Equations
TL;DR: These lecture notes are an edited subset of material from graduate courses given by the author at the universities of Utah and Minnesota and at Concordia University, and from short courses given at various institutions, including the Universite Pierre et Marie Curie (Paris VI), the Centre de Recherches Mathematiques of the University of Montreal, the Technische Universitat Hamburg-Harburg, and the Benemerita Universidad Autonoma de Puebla.
Journal ArticleDOI
Homoclinic bifurcation at resonant eigenvalues
TL;DR: In this paper, the authors consider a bifurcation of homoclinic orbits, which is an analogue of period doubling in the limit of infinite period, and show that it can occur in generic two parameter vector fields with resonant eigenvalues, where the resonance condition requires the eigen values with positive/negative real part closest to zero to be real, simple and equidistant to zero.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Journal ArticleDOI
The Von Karman Swirling Flows
TL;DR: Computations of the Karman swirling flows are reported in this paper, which clearly indicate that an infinite sequence of Karman swirlings exists and can be found in time O(n 2 ).
Journal ArticleDOI
The Numerical Solution of Boundary Value Problems with an Essential Singularity
Frank de Hoog,Richard Weiss +1 more
TL;DR: In this paper, the numerical solution by two difference schemes (box, trapezoidal) of boundary value problems for first order systems of ordinary differential equations with a singularity of the second kind is investigated.