‘Numerical methods in fracture mechanics’ proceedings of the 4th international conference. Ed. A. R. Luxmoore, D. R. J. Owen, Y. P. D. Rajapakse and M. F. Kanninen, Pineridge Press, Swansea (1987)

Abstract

BOOK REVIEWS597 and numerical integration. These two texts are, in most respects, similar but describe more sophisticated software for use on a personal computer. The emphasis is on computer programs, user interfaces (for the Apple and IBM) and program operations, with a brief description of numerical techniques.The two books differ only in the example computer programs written specifically for the Apple and IBM PC computers (they are referred to henceforth as 'the book). The text consists of eight chapters: on interpolation, complex arithmetic, vector and matrix operations, solution of simultaneous equations, solution of equations, integration, differential equations, and curve fitting. Each chapter contains a number of computer codes, with a total of about twenty.The details of each computer code are contained in the program listing, followed by a program description and program operation with example menus, user inputs and program outputs. The listings are clear, with an abundance of comment statements to assist the reader. The program description includes details of the tasks performed by each subroutine, and all input and output variables are defined. There follows a detailed explanation of how to run the program; this is obviously specific to the Apple and IBM PC computers. The details of the programs, subroutines, and user input and output provide a model format for program documentation and can be recommended to all writers of software.Details of the numerical methods discussed in the book are kept to a minimum. The reader is referred to the abundance of books which discuss in depth the question of numerical analysis.From the elementary nature of the numerical routines, the book is clearly aimed at the non-numerical specialist who is interested in results rather than methods. To achieve success the details and explanations of the methods should be particularly good.However, I found the text to contain numerous typing errors and in some cases misleading explanations of basic concepts. Certainly the standard of proof-reading does not approach the level expected of a textbook. There are numerous errors with subscripts and superscripts, brackets in equations are occasionaly missing, there are simple arithmetic mistakes in the solution to problems, and throughout the abbreviation for logarithm is given as 'ln'. But of more concern are misleading statements, of which there are several. To take a particularly bad example, the errors contained in the discussion on how to form the product of two matrices destroy the explanation.The issue of clarity is not helped by a rather strange mixture of typefaces. The diagrams are printed in a style I found uncomfortable to the eye, and the typeface for the program descriptions and operations is difficult to read and not conducive to continued concentration.Many of the errors are obvious and can be immediately corrected, but one cannot help wondering if there are similar types of errors in the program listings. If so, the unsuspecting user of the software will have a frustr...

Sheath and presheath dynamics in plasma immersion ion implantation

“…The transit time of the sheath at different distances was defined as the time at which the electron density dropped to 5% of the initial value. For the theoretical fit the differential equation ( 10) was solved with a predictor-corrector algorithm with a variable step width [25]. The parameters used for the calculations were n 0 = 5 × 10 10 cm −3 (planar) and 4 × 10 10 cm −3 (spherical), L = 50 mm and kT e = 1 eV.…”

A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis

“…Root-finding methods are essential in various scientific disciplines for solving nonlinear systems, which are systems of equations that cannot be represented as linear combinations of their inputs. These techniques, which include Newton's method, the bisection method, and the secant method, are used to determine solutions to equations where the function is zero, called [1] roots. Engineering relies on the use of equations to address the qualities of materials and forces, which are crucial to the design of systems and structures.…”

“…There exists a continuous operator, Φ : D ⊂ S ′ , in Equation (1). This operator is defined on a nonempty convex subset D of a Banach space S and has values in a Banach space S ′ .…”

“…This operator is defined on a nonempty convex subset D of a Banach space S and has values in a Banach space S ′ . This investigation aims to determine an approximation of the unique local solution al pha ∈ S for the problem stated in (1). In the one-dimensional example, Banach spaces are equivalent to S = S ′ = R. The problem can be reduced to approximating a single local root…”

Fracture behaviour analysis of artificial hip biomaterials

“…[148][149] [152] Moguće je korišćenje i drugih oblika epruveta, pod određenim uslovima, kada se zapravo primenjuje modifikacija standardom definisanih epruveta.…”