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Adjoint Equations and Analysis of Complex Systems: (295 Mathematics and Its Applications)

Adjoint Equations and Analysis of Complex Systems: (295 Mathematics and Its Applications)


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About the Book

This monograph presents the fundamentals of adjoint equation theory and perturbation algorithms, exemplifying their applications by solutions of complex problems of mathematical physics. The earlier Russian version (1992) has been completely revised and supplemented with many new results for this edition, thus offering a unique compilation of the author's research in many areas of applied mathematics over the years. The first part of the book describes the theory of adjoint equations and perturbation algorithms and gives examples of applications to problems. Nonlinear problems and statements of inverse problems based on methods of adjoint equations and perturbation are considered. The second part focuses on the applications of adjoint equations theory and perturbation algorithms to the solution of concrete problems, such as global and regional environmental protection, interaction between atmosphere and ocean, and data assimilation problems. This volume should be of value to a wide range of researchers, workers and engineers interested in creating new technologies for designing and planning experiments, while solving concrete problems, especially for those working on numerical mathematics.

Table of Contents:
I. Adjoint Equations and Perturbation Theory.- 1. Main and Adjoint Equations. Perturbation Theory.- 2. Simple Main and Adjoint Equations of Mathematical Physics.- 3. Nonlinear Equations.- 4. Inverse Problems and Adjoint Equations.- II. Problems of Environment and Optimization Methods on the Basis of Adjoint Equations.- 5. Analysis of Mathematical Models in Environmental Problems.- 6. Adjoint Equations, Optimization.- 7. Adjoint Equations and Models of General Circulation of Atmosphere and Ocean.- 8. Adjoint Equations in Data Processing Problems.- Appendix I: Splitting Methods in the Solution of Global Problems.- 1. Splitting Methods for Solution of Non-Stationary Problems.- 2. Multicomponent Splitting of Problems.- 3. An Example of Application: Two-Dimensional Problem with Constant Coefficients.- Appendix II: Difference Analogue of Non-Stationary Heat Diffusion Equation in Atmosphere and Ocean.


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Product Details
  • ISBN-13: 9780792330134
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 297 mm
  • No of Pages: 468
  • Returnable: Y
  • Width: 210 mm
  • ISBN-10: 0792330137
  • Publisher Date: 31 Jan 1995
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 295 Mathematics and Its Applications


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Adjoint Equations and Analysis of Complex Systems: (295 Mathematics and Its Applications)
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