Classical Fortran

Classical FORTRAN: Programming for Engineering and Scientific Applications, Second Edition teaches how to write programs in the Classical dialect of FORTRAN, the original and still most widely recognized language for numerical computing. This edition retains the conversational style of the original, along with its simple, carefully chosen subset la

Classical FORTRAN is a college text, self-study guide, and reference about computer programming for numerical calculations. The book features a conversational, classroom-proven style that is easy to read and contains numerous case studies and examples. The author provides practical advice on program design, documentation, and coding style and unusu

Numerical software is used to test scientific theories, design airplanes and bridges, operate manufacturing lines, control power plants and refineries, analyze financial derivatives, identify genomes, and provide the understanding necessary to derive and analyze cancer treatments. Because of the high stakes involved, it is essential that results computed using software be accurate, reliable, and robust. Unfortunately, developing accurate and reliable scientific software is notoriously difficult. This book investigates some of the difficulties related to scientific computing and provides insight into how to overcome them and obtain dependable results. The tools to assess existing scientific applications are described, and a variety of techniques that can improve the accuracy and reliability of newly developed applications is discussed. Accuracy and Reliability in Scientific Computing can be considered a handbook for improving the quality of scientific computing. It will help computer scientists address the problems that affect software in general as well as the particular challenges of numerical computation: approximations occurring at all levels, continuous functions replaced by discretized versions, infinite processes replaced by finite ones, and real numbers replaced by finite precision numbers. Divided into three parts, it starts by illustrating some of the difficulties in producing robust and reliable scientific software. Well-known cases of failure are reviewed and the what and why of numerical computations are considered. The second section describes diagnostic tools that can be used to assess the accuracy and reliability of existing scientific applications. In the last section, the authors describe a variety of techniques that can be employed to improve the accuracy and reliability of newly developed scientific applications. The authors of the individual chapters are international experts, many of them members of the IFIP Working Group on Numerical Software.

Publisher Description

Today, people use a large number of "systems" ranging in complexity from washing machines to international airline reservation systems. Computers are used in nearly all such systems: accuracy and security are becoming increasingly essential. The design of such computer systems should make use of development methods as systematic as those used in other engineering disciplines. A systematic development method must provide a way of writing specifications which are both precise and concise; it must also supply a way of relating design to specification. A concise specification can be achieved by restricting attention to what a system has to do: all considerations of implementation details are postponed. With computer systems, this is done by: 1) building an abstract model of the system -operations being specified by pre-and post-conditions; 2) defining languages by mapping program texts onto some collection of objects modelizing the concepts of the system to be dealt with, whose meaning is understood; 3) defining complex data objects in terms of abstractions known from mathematics. This last topic, the use of abstract data types, pervades all work on specifications and is necessary in order to apply ideas to systems of significant complexity. The use of mathematics based notations is the best way to achieve precision. 1.1 ABSTRACT DATA TYPES, PROOF TECHNIQUES From a practical point of view, a solution to these three problems consists to introduce abstract data types in the programming languages, and to consider formal proof methods.

Comprises 10 contributions that summarize the state of the art in the areas of high performance solutions of structured linear systems and structured eigenvalue and singular-value problems. Topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. Specific paper topics include: the stable parallel solution of general narrow banded linear systems; efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form; a numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems; and parallel CG-methods automatically optimized for PC and workstation clusters. Annotation copyrighted by Book News, Inc., Portland, OR

By modern analytic mechanics we mean the classical mechanics of today, that is, the mechanics that has proven particularly useful in understanding the universe as we experience it from the solar system, to particle accelerators, to rocket motion. The mathematical and numerical techniques that are part of this mechanics that we present are those that we have found to be particularly productive in our work in the subject. The balance of topics in this book is somewhat different from previous texts. We emphasize the use of phase space to describe the dynamics of a system and to have a qualitative understanding of nonlinear systems. We incorporate exercises that are to be done using a computer to solve linear and nonlinear problems and to have a graphical representation of the results. While analytic solutions of physics problems are to be prefer. red, it is not always possible to find them for all problems. When that happens, techniques other than analysis must be brought to bear on the problem. In many cases numerical treatments are useful in generating solutions, and with these solutions often come new insights. These insights can sometimes be used for making further analytic progress, and often the process is iterative. Thus the ability to use a computer to solve problems is one of the tools of the modern physicist. Just as analytic problem-solving enhances the student's understanding of physics, so will using the computer enhance his or her appreciation of the subject.

These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various