Numerical Methods for Solving Inverse Problems of Mathematical Physics
In this monograph, the authors consider the main classes of inverse problems in mathematical physics and their numerical treatment. They include in the book many numerical illustrations and codes for their realization. They give a rather complete treatment of basic difficulties for approximate solutions of inverse problems. They use minimal mathematical apparatus (in particular, basic properties of operators in finite-dimensional spaces). Russian mathematicians contributed in a substantial way to solutions of theoretical and practical questions studied in inverse problems in mathematical physics (pioneering work in this direction was done by Andrei Nikolaevich Tikhonov).
The main topics treated in the book are boundary value problems for ordinary differential equations and elliptic and parabolic partial differential equations, methods of solutions for ill-posed problems and evolutionary inverse problems. The book is intended for graduate students and scientists interested in applied mathematics, computational mathematics and mathematical modelling.