To: “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering” (Walter L. Anderson, GEOPHYSICS, July 1979, p. 1287–1305)

Geophysics ◽  
1979 ◽  
Vol 44 (10) ◽  
pp. 1769-1769
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Digital Filtering ◽  
Hankel Transforms ◽  
Recent Computer

The author of the recent computer program, “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering” (Walter L. Anderson, Geophysics, July 1979 p. 1287–1305) wishes to correct the following errors. On p. 1290, under FUN =, the use of brackets is incorrect as appearing in: FUN = CMPLX[F1(G), 0.0] and FUN = CMPLX[F1(G),F2(G)].The correct Fortran notation should use parentheses as: FUN = CMPLX(F1(G),0.0) and FUN = CMPLX(F1(G),F2(G)). On p. 1291, the DO statement appears incorrectly as: Do 1 I-1, NSAVE Insert code to modify FSAVE in COMMON for a related kernel; for example, if ZF2(G) = G*ZF1(G), use the code; if 1 FSAVE (I) = GSAVE(I)*FSAVE(I) The correct DO statement should be: DO 1 I = 1,NSAVE Insert code to modify FSAVE in COMMON for a related kernel; for example, if ZF2(G( = G*ZF1(G), then use the following code, 1 FSAVE(I) = GSAVE(I)*FSAVE(I)

Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1287-1305 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Large Range ◽  
Digital Filtering ◽  
Hankel Transform ◽  
Kernel Functions ◽  
General Nature ◽  
Earth Model ◽  
Hankel Transforms ◽  
Quadrature Methods ◽  
Test Driver ◽  
Different Order

A linear digital filtering algorithm is presented for rapid and accurate numerical evaluation of Hankel transform integrals of orders 0 and 1 containing related complex kernel functions. The kernel for Hankel transforms is defined as the non‐Bessel function factor of the integrand. Related transforms are defined as transforms, of either order 0 or 1, whose kernel functions are related to one another by simple algebraic relationships. Previously saved kernel evaluations are used in the algorithm to obtain rapidly either order transform following an initial convolution operation. Each order filter is designed with identical abscissas over a large range so that an adaptive convolution procedure can be applied to a large class of kernels. Different order Hankel transforms with related kernels are often found in electromagnetic (EM) applications. Because of the general nature of this algorithm, the need to design new filters should not be necessary for most applications. Accuracy of the filters is comparable to that of single‐precision numerical quadrature methods, provided well‐behaved kernels and moderate values of the transform argument are used. Filtering errors of less than 0.005 percent are demonstrated numerically using known analytical Hankel transform pairs. The digital filter accuracy is also illustrated by comparison with other published filters for computing the apparent resistivity for a Schlumberger array over a horizontally layered earth model. The algorithm is written in Fortran IV and is listed in the Appendix along with a test driver program. Detailed comments are included to define sufficiently all calling parameter requirements.

COPOINT – a simple computer program to determine copolymerization parameters by numerical integration

e-Polymers ◽  
2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Uwe Beginn
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Differential Form ◽  
Statistical Error ◽  
Monomer Conversion ◽  
Quadratic Approximation ◽  
Copolymer Composition ◽  
Composition Data ◽  
Simple Computer ◽  
Broad Variety

AbstractA computer program is introduced that evaluates the parameters of binary copolymerizations from comonomer/copolymer composition data as obtained from polymerization experiments with finite monomer conversion. The program numerically integrates a given copolymerization equation in its differential form and can be applied to a broad variety of functions. Copolymerization parameters are obtained by minimizing the sum of square differences between measured and calculated polymer compositions with respect to the copolymerization parameters. Errors of the fitted parameters are estimated from the statistical error of the sum of square differences, as well as from a quadratic approximation of this sum in the vicinity of the optimized values of the copolymerization parameters.

scholarly journals The Split Comets: Gravitational Interaction Between the Fragments

1979 ◽  
Vol 81 ◽  
pp. 311-314
Author(s):  
Z. Sekanina
Keyword(s):  
Gravitational Field ◽  
Computer Program ◽  
Numerical Integration ◽  
Relative Motion ◽  
Gravitational Interaction ◽  
Parent Nucleus ◽  
The Other ◽  
Comet Nucleus

The n-body computer program by Schubart and Stumpff (1966) has been slightly modified to study the gravitational interaction between two fragments of a split comet nucleus in the sun's gravitational field. All calculations refer to the orbit of Comet West (1976 VI), the velocity of separation of the fragments is assumed to be equal in magnitude to the velocity of escape from the parent nucleus, and the numerical integration of the relative motion of one fragment (called the companion) with respect to the other (principal fragment) is carried over the period of 200 days from separation.

scholarly journals Analysis of progress curves by simulations generated by numerical integration

1989 ◽  
Vol 258 (2) ◽  
pp. 381-387 ◽  
Author(s):  
C T Zimmerle ◽  
C Frieden
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Rate Constants ◽  
Weighted Least Squares ◽  
Rate Equations ◽  
Kinetic Rate ◽  
Fitting Procedure ◽  
Progress Curve ◽  
Kinetic Rate Constants ◽  
Simulated Test

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.

Digital Filtering — An Interactive Computer Program for the Design and Simulation of a Finite Impulse Response (F.I.R.) Digital Filter

1986 ◽  
Vol 23 (4) ◽  
pp. 339-348 ◽  
Author(s):  
I. M. Longair
Keyword(s):  
Computer Program ◽  
Impulse Response ◽  
Digital Filter ◽  
Finite Impulse Response ◽  
Digital Filtering ◽  
Interactive Computer Program ◽  
Electronic Engineering ◽  
Low Pass ◽  
Computer Based ◽  
Fir Digital Filter

Digital filtering techniques have become an important part of the curriculum of electronic engineering courses. This paper details a computer-based teaching aid, for the popular BBC model B microcomputer, which may be used to design and display the characteristics of a low-pass finite impulse response (FIR) digital filter.

APL Computer Program for the Analytical and Numerical Integration of Hormonal Disappearance Data

1972 ◽  
Vol 50 (8) ◽  
pp. 845-852 ◽  
Author(s):  
Maurice Normand
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Programming Language ◽  
Biomedical Applications

The biomedical applications of a new programming language characterized by simplicity and economy of symbols and coupled with access to remote terminals are illustrated by the description and analysis of a program pertaining to the lengthy computations involved in certain aspects of hormonal kinetics and their statistical correlates.

scholarly journals Berechnung von Eigensdiaften zweiatomiger Moleküle Ein- und Zweizentrenintegrale mit Slater-Funktionen / Calculation of Properties of Diatomic Molecules. One and Two Center Integrals Using Slater Type Orbitals

1973 ◽  
Vol 28 (2) ◽  
pp. 142-173
Author(s):  
Otto Hell ◽  
Hans Knof
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Computer Programs ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Analytical Treatment ◽  
Program Logic ◽  
Modern Computer ◽  
Numerical Integrations ◽  
The One

The methods for evaluation of two center integrals by use of Slater functions originate from the time of desk calculators, although they were later adapted to computers. This paper gives an analytical treatment of these integrals, in preparation for a modern computer program. The sixfold two electron two center integrals require only one numerical integration in case of the exchange integrals, and in case of the Coulomb and hybrid integrals two numerical integrations are required. The one center integrals and all the one electron integrals are solved fully analytically. This makes the analysis and program logic more lucid.All the special conditions arising during evaluation of the integrals are described in detail so that this paper should suffice as a basis for writing computer programs to evaluate such integrals.

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