TY  - BOOK
AU  - Kabanikhin,Sergey I.
AU  - Satybaev,Abdigany D.
AU  - Shishlenin,Maxim A.
TI  - Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
T2  - Inverse and Ill-Posed Problems Series
SN  - 9783110960716
AV  - QA371 .K18 2005 
PY  - 2004///
CY  - Berlin/Boston
PB  - De Gruyter, Inc.
KW  - Inverse problems (Differential equations)--Numerical solutions
KW  - Finite differences
KW  - Electronic books
N1  - Intro -- Main definitions and notations -- Introduction -- Chapter 1. Finite-difference scheme inversion (FDSI) -- 1.1. Introduction -- 1.2. Volterra operator equations -- 1.3. Definitions and examples -- 1.4. Convergence of FDSI -- 1.5. Numerical examples -- Chapter 2. Linearized multidimensional inverse problem for the wave equation -- 2.1. Introduction -- 2.2. Problem formulation -- 2.3. Linearization -- 2.4. Analyzing the structure of the solution to one-dimensional direct problem -- 2.5. Existence theorem for the direct problem -- 2.6. Uniqueness of solutions to the inverse problem and regularization -- 2.7. Numerical examples -- Chapter 3. Methods of I. M. GePfand, B. M. Levitan and M. G. Krein -- 3.1. Introduction -- 3.2. Gel'fand-Levitan-Krein (GLK) equation for one-dimensional inverse problem -- 3.3. Multidimensional analog of GLK-equations -- 3.4. Gel'fand-Levitan method for wave equation -- 3.5. Discrete analog of the Gel'fand-Levitan equation -- 3.6. Multidimensional discrete analog -- 3.7. Numerical examples -- Chapter 4. Boundary control method (BC method) -- 4.1. Introduction. Statement of the problem -- 4.2. BC method in one-dimensional case -- 4.3. BC method for 2D acoustic inverse problem -- 4.4. Numerical examples -- Chapter 5. Projection method -- 5.1. Introduction -- 5.2. Projection method for solving inverse problem for the wave equation -- 5.3. Projection method for solving inverse acoustic problem -- 5.4. Numerical examples -- Appendix A -- Appendix B -- Bibliography
N2  - The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4008727
ER  -