© 1995

Adjoint Equations and Analysis of Complex Systems


Part of the Mathematics and Its Applications book series (MAIA, volume 295)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Introduction

    1. Guri I. Marchuk
      Pages 1-5
  3. Adjoint Equations and Perturbation Theory

    1. Front Matter
      Pages 7-8
    2. Guri I. Marchuk
      Pages 123-162
    3. Guri I. Marchuk
      Pages 163-205
  4. Problems of Environment and Optimization Methods on the Basis of Adjoint Equations

    1. Front Matter
      Pages 207-211
    2. Guri I. Marchuk
      Pages 269-325
    3. Guri I. Marchuk
      Pages 389-421
  5. Back Matter
    Pages 422-468

About this book


New statements of problems arose recently demanding thorough ana­ lysis. Notice, first of all, the statements of problems using adjoint equations which gradually became part of our life. Adjoint equations are capable to bring fresh ideas to various problems of new technology based on linear and nonlinear processes. They became part of golden fund of science through quantum mechanics, theory of nuclear reactors, optimal control, and finally helped in solving many problems on the basis of perturbation method and sensitivity theory. To emphasize the important role of adjoint problems in science one should mention four-dimensional analysis problem and solution of inverse problems. This range of problems includes first of all problems of global climate changes on our planet, state of environment and protection of environ­ ment against pollution, preservation of the biosphere in conditions of vigorous growth of population, intensive development of industry, and many others. All this required complex study of large systems: interac­ tion between the atmosphere and oceans and continents in the theory of climate, cenoses in the biosphere affected by pollution of natural and anthropogenic origin. Problems of local and global perturbations and models sensitivity to input data join into common complex system.


Mathematica algorithm algorithms calculus complex systems optimization

Authors and affiliations

  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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