Showing papers in "Siam Review in 1983"
TL;DR: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes.
Abstract: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is given to the Godunov-type schemes that result from using an approximate solution of the Riemann problem. For schemes based on flux splitting, the approximate Riemann solution can be interpreted as a solution of the collisionless Boltzmann equation.
3,133 citations
1,002 citations
TL;DR: Many generalizations of these ideas seem to possess a similar elegant mathematical structure and a brief descriptive review of these developments is given in this paper, where a rigorous version of an engineering folk theorem called the $2WT$-Theorem is presented.
Abstract: Investigation of the problem of simultaneously concentrating a function . and its Fourier transform has led to some interesting special functions that have widespread applications in engineering. They provide a means of proving a rigorous version of an engineering folk theorem called the $2WT$-Theorem. Many generalizations of these ideas seem to possess a similar elegant mathematical structure. A brief descriptive review is given of these developments.
588 citations
TL;DR: This paper surveys the applications, methods and theory of sequence comparison, which incorporate two basic ideas a systematic concept of distance between sequences, and elegant recursive algorithms for doing the necessary computations.
Abstract: A wide variety of different applications lead to problems in which sequences of different lengths must be compared, to see how different they are, and to see which elements in one sequence correspond to which elements in the other sequence. Successful methods for handling these problems been repeatedly reinvented which incorporate two basic ideas a systematic concept of distance between sequences, and elegant recursive algorithms for doing the necessary computations. The major application areas are speech processing and macromolecular biology. Computer science is another significant application area, and applications have also been made to bird song, handwriting analysis, gas chromatography, geological strata, and text collation. This paper surveys the applications, methods and theory of sequence comparison.
396 citations
TL;DR: In this article, an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth, and the ensuing particle velocity at the surface is assumed to be measured.
Abstract: An impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth. The ensuing particle velocity at the surface is assumed to be measured. The problem...
242 citations
69 citations
59 citations
TL;DR: A brief review of recent advances in the field of wave propagation in periodic structures is made in this paper, focusing on the application of, the method of multiple scales to a class of problems in...
Abstract: A brief review of recent advances in the field of wave propagation in periodic structures is made. The review focuses on the application of, the method of multiple scales to a class of problems in ...
52 citations
52 citations
TL;DR: While in many programs, the use of an AQR can save significant human time, in many other programs, its use can be a disaster.
Abstract: Numerical quadrature is required as a component in many large scale (and small scale) scientific programs. Frequently the scientist faces a choice. Either he may use one of the comparatively recent automatic quadrature routines (AQR) or he may use a standard rule evaluation quadrature routine (REAR) based directly on traditional formulae. The purpose of this article is to help the scientist to make an informed choice.In the first half of this article we introduce some generic properties of AQRs. The more straightforward of these are those concerned with reliability and economy. Less straightforward is the vital “performance profile” property. The second half of this article is devoted principally to demonstrating how in some calculations the jagged performance profile associated with the AQR can cause other parts of the overall program to be far more expensive than necessary. Thus, while in many programs, the use of an AQR can save significant human time, in many other programs, its use can be a disaster....
50 citations
TL;DR: In this paper, the authors assess the present status and future prospects of numerical fluid dynamics, through a series of case studies, and briefly review the gradual disintegration of Euler's concept of analytical fluid dynamics as a mathematical science.
Abstract: By 1755, Euler was explicitly envisaging analytical fluid dynamics as a mathematical science, that of integrating the Euler–Lagrange equations. But by 1915, at least seven different analytical models were being used to explain the behavior of real fluids. From 1945 on, von Neumann was trying to “arithmetize” the approximate solution of the equations associated with these models, with the help of large-scale, high-speed computers. Thus he was envisaging numerical fluid dynamics as a mathematical science.After briefly reviewing the gradual disintegration of Euler’s concept of analytical fluid dynamics as a mathematical science, this survey article tries to assess the present status and future prospects of numerical fluid dynamics, through a series of case studies.
TL;DR: This paper identifies three principal sources of variability in dynamic storage allocation that need to be addressed in the coming generation of smart grids.
Abstract: In computer science, dynamic storage allocation refers to the mechanisms for managing primary and secondary storage under a fluctuating demand In this paper we identify three principal sources of
TL;DR: In this paper, singular perturbation techniques are used to study the effects of toxicity on population growth in a closed system with respect to the usual terms of the logistic equation, and two major types of systems are discovered, those with populations immediately sensitive to toxins and those that succumb to toxins only after long times.
Abstract: Volterra’s model for population growth in a closed system includes an integral term to indicate accumulated toxicity in addition to the usual terms of the logistic equation. Solutions to this equation are studied by means of singular perturbation techniques. Two major types of systems are discovered, those with populations immediately sensitive to toxins and those that succumb to toxins only after long times.
TL;DR: Ito's stochastic calculus has been used in the theory of finance from the perspective of continuous time as mentioned in this paper, and the use of Ito's calculus in modern financial theory is illustrated by expositing a few representative applications.
Abstract: This paper presents an introduction to Ito’s stochastic calculus by stating some basic definitions, theorems and mathematical examples. Afterwards, the use of Ito’s calculus in modern financial theory is illustrated by expositing a few representative applications. The main observation of this paper is that Ito’s calculus which was developed from purely mathematical questions originating in Wiener’s work has found unexpectedly important applicability in the theory of finance from the perspective of continuous time.
TL;DR: In this paper, the authors introduce the notion of elasticity and present its main mathematical and graphical properties, illustrating them on real economic cases, such as the consumption of marijuana and the demand for hospital beds.
Abstract: The following pages introduce the notion of elasticity and present its main mathematical and graphical properties, illustrating them on real economic cases, such as the consumption of marijuana and the demand for hospital beds.
TL;DR: Two fundamental problems in estimating human risk from environmental carcinogens on the basis of studies with laboratory animals, the low-dose extrapolation problem and the mouse-to-man problem, are described.
Abstract: Two fundamental problems in estimating human risk from environmental carcinogens on the basis of studies with laboratory animals, the low-dose extrapolation problem and the mouse-to-man problem, are described. Dichotomous dose-response models and time-to-response models for toxicological dose-response experiments are reviewed and compared; various mathematical methods of effecting the low-dose extrapolation are summarized. The relevance of other important factors, such as pharmacokinetic information, environmental and genetic heterogeneity and considerations of the carcinogenic mechanism, is also discussed.
TL;DR: In this article, a general transformation for finding a multiple zero of a function f is presented, which is based on transforming f to a function T for which $x^ * $ is a simple zero.
Abstract: Many methods for finding a multiple zero $x^ * $ of a function f are based on transforming f to a function T for which $x^ * $ is a simple zero. We give and analyze a general transformation which i...
TL;DR: Given the locus of the path travelled by the front wheels of a bus, a differential equation describing the path of the rear wheels is derived which explicitly solve in the case of a straight line and a circle.
Abstract: Given the locus of the path travelled by the front wheels of a bus, we derive a differential equation describing the path of the rear wheels which we explicitly solve in the case of a straight line and a circle. These solutions can be applied to such specific problems as a bus turning a corner or a bus changing lanes.
TL;DR: In this paper, an elementary introduction to linear Volterra integral and integro-differential equations is presented, and it is demonstrated that the theory of existence, uniqueness, dimensionality of the solution space, and the variation of parameters formula are virtually indistinguishable from the corresponding elementary theory of ordinary differential equations.
Abstract: This paper presents an elementary introduction to linear Volterra integral and integro-differential equations. It is demonstrated that the theory of existence, uniqueness, dimensionality of the solution space, and the variation of parameters formula are virtually indistinguishable from the corresponding elementary theory of ordinary differential equations. A review of some current problems is also included.
TL;DR: In this article, the location of roots of polynomials with respect to the principal coordinate axes (referred to generally as the Routh-Hurwitz criteria and the Sturm criteria) is investigated.
Abstract: This paper concerns the location of roots of polynomials with respect to the principal coordinate axes (referred to generally as the Routh–Hurwitz criteria and the Sturm criteria). It provides a new proof of the results established by Wall and Frank which relate the number of positive and negative coefficients in a continued fraction to the number of roots of a polynomial in the left half plane and right half plane. It extends these results to locate the number of real roots of real polynomials on the positive or negative real axis. The paper also provides some miscellaneous criteria so that selected parts of a polynomial may be analyzed in order to determine the number of roots in a half plane.