Synthesis of adequate mathematical description of physical processes / Yuri Menshikov.

Format:

Book

Author/Creator:

Menshykov, Yurii, author.

Language:

English

Subjects (All):

Mathematical models.

Physical Description:

1 online resource (viii, 154 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Newcastle upon Tyne, England : Cambridge Scholars Publishing, [2020]

Summary:

For effective use of the results of computational calculations, it is necessary that the computational schemes used correspond to real physical processes, so that the schemes are adequate. The issue of adequacy is currently poorly understood and there are also no generally accepted criteria of adequacy.This book is the first to address the questions of constructing adequate mathematical descriptions of physical processes and their reasonable use in the future for various purposes. It proposes two adequacy criteria (quantitative and qualitative), and describes several possible algorithms for synthesis of cases when the physical process is composed of a system of ordinary differential equations or a mathematical model in algebraic form. The algorithms described here will be useful for specialists in areas where methods of mathematical modeling are used, such as mechanics.

Contents:

Intro

Contents

Abstract

Foreword

Introduction

1. General Questions on the Mathematical Simulation of Physical Processes

1.1. Mathematical simulation and its role in the study of physical processes

1.2. The process of constructing mathematical descriptions (2 approaches)

1.3. The adequacy of mathematical descriptions of natural processes

2. Examples of the Synthesis of Mathematical Descriptions with the Estimation of Adequacy

2.1. Mathematical simulation of system dynamics

2.2. Mathematical vortex model of planetary systems

2.3. Mathematical modelling of tectonic processes

2.4. Simulation of emotional dynamics

3. Problems of Synthesizing Adequate Mathematical Descriptions by Ordinary Differential Equations

3.1. Definition of adequate mathematical description of quantitative type

3.2 Definition of adequate mathematical description of qualitative type

3.3. Obtaining Basic Equations

3.4. Specific features of the solution of integral equations in synthesis problems

4. Algorithms for Obtaining Solutions

4.1. Variational method

4.2. Selection of functional of quality

4.3. Synthesis of stable adequate mathematical descriptions for class operators

4.4. Objectively checking the adequacy of mathematicaldescriptions for inexact operators

4.4. Objectively checking the adequacy of mathematical descriptions for inexact operators

4.5. Uncontrolled errors in initial conditions

4.6. The problem of forecasting physical characteristics

4.7. Adequate mathematical descriptions in the problem of motion control

5. Synthesis of Adequate Mathematical Descriptions in Algebraic Form

5.1. Peculiarities of statements of similar-type problems

5.2. Definition of adequate mathematical descriptions in algebraic forms.

5.3. Algorithms of parameter identification of adequate linear mathematical models in algebraic form

5.4. Synthesis of an adequate mathematical model of the steel smelting process

5.5. Synthesis of an adequate mathematical model of the economic process

Conclusion

Future Research Directions

References

Appendix A.

Notes:

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-5275-5797-9

OCLC:

1195824889