Modelling Methods in Scientific Computation

About this book

Features: Examines inverse type problems and stochastic modelling; Three appendices provide a concise guide to functional analysis, approximation theory and probability; Includes a diskette containing ten scientific programs to introduce the reader to scientific computation at a practical level.

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 Stochast ic 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

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