Modelling mathematical methods and scientific computation

Author(s)

• Bellomo, Nicola
• Preziosi, Luigi

Bibliographic Information

Modelling mathematical methods and scientific computation

Nicola Bellomo, Luigi Preziosi

（Mathematical modelling series）

CRC Press, 1995

Note

Includes bibliographical references (p. 481-489) and index

System requirements for accompaning computer disk: IBM compatible system

Description and Table of Contents

Description

Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

Table of Contents

Preface Mathematical Modelling Introduction Definition of Mathematical Modelling Classification of Mathematical Modelling Modelling Methods Validation of Mathematical Models Mathematical Modelling as a Science Discrete Models Plan of Chapter 2 About Mathematical Modelling Mathematical Formulation of Problems On Existence, Uniqueness and Continuity Linear Systems Stability and Linearization From Bifurcation to Chaos Numerical Methods for Initial Value Problems Scientific Programs Continuous Models Introduction Mathematical Modelling Equilibrium Equation for the Vibration of an Elastic String Mathematical Models of Continuum Mechanics Mathematical Models of Electromagnetism Direct Simulation Models in Biology Classification and Characteristics Mathematical Formulation of Problems Finite Difference Methods The Collocation Method Decomposition of Domains Applications and Scientific Programs Inverse and Stochastic Problems Inverse Problems and Stochastic Models Classification of Inverse Problems Solution by Decomposition of Domains Solution by Minimization Techniques Mathematical Modelling and Stochasticity Classification of Discrete Stochastic Models Classification of Continuous Stochastic Models Modelling and Solution of Problems Stochastic Aspects and Inverse Problems Kinetic Models Application Discussion and Developments Scientific Programs Appendix 1. Functional Spaces and Fixed Point Theorems Appendix 2. Interpolation and Approximation Appendix 3. Random Variables References Subjects Index

by "Nielsen BookData"

Details

• NCID: BA24647713
• ISBN:
  • 0849383315
• LCCN: 94038722
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: xiv, 497 p.
• Size: 24 cm
• Attached Material: 1 floppy disk (3 1/2 in.)
• Classification:
  • LCC : QA401
  • DC20 : 501/.1
• Subject Headings:
  • LCSH : Mathematical models
• Parent Bibliography ID:
  • BA24647870