Numerical Methods of Mathematics Implemented in Fortran
Название: Numerical Methods of Mathematics Implemented in Fortran
Автор: Sujit Kumar Bose
Формат: PDF, DJVU
Размер: 10.1 MB
Год издания: 2019
The computer codes have been written in the Fortran programming language, which is the traditional language for scientific computation. Fortran has a vast repository of source codes used in real-world applications and has continuously been upgraded in line with the computing capacity of the hardware. The language is fully backwards compatible with its earlier versions, facilitating integration with older source codes.
For writing the computer codes, I have chosen to use the Fortran programming language. Fortran is a powerful, easy-to-learn and traditional language for scientific computation in which there are a number of inbuilt intrinsic functions. The present version Fortran 2003 is fully backwards-compatible with its earlier popular versions FORTRAN 77 and Fortran 90/95. The language has been upgraded to Fortran 2010, and a future version Fortran 2018 is proposed to be launched during this year.
The latest versions are the only ones usable in supercomputers and in modern multiprocessor desktops. There is, therefore, some merit in retaining Fortran for the purpose of scientific computation, especially because of the fact that a large number of source codes mentioned in book are written in that language.
The Fortran source codes are transparent and can be modified whenever required. Finally, it is interoperable by binding with programs written in other languages, such as C, PYTHON and MATLAB. Being a language oriented towards scientific computations, it handles complex valued functions easily, a facility not available in JAVA. An assessment states that Fortran source codes can be faster in execution by as much as 30%, compared to source codes written in other languages. The saving in execution time is therefore substantial for large programs.
This book systematically classifies the mathematical formalisms of computational models that are required for solving problems in mathematics, engineering and various other disciplines. It also provides numerical methods for solving these problems using suitable algorithms and for writing computer codes to find solutions. For discrete models, matrix algebra comes into play, while for continuum framework models, real and complex analysis is more suitable. The book clearly describes the method–algorithm–code approach for learning the techniques of scientific computation and how to arrive at accurate solutions by applying the procedures presented. It not only provides instructors with course material but also serves as a useful reference resource. Providing the detailed mathematical proofs behind the computational methods, this book appeals to undergraduate and graduate mathematics and engineering students.
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