This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and...

Li and Ito, both affiliated with the Department of Mathematics and the Center for Scientific Computing at North Carolina State University, introduce the immersed interface method (IIM), a numerical method for solving materials interface problems and proble

This comprehensive monograph analyses Lagrange multiplier theory, which provides a tool for the analysis of a general class of nonlinear variational problems, and is the basis for developing efficient and powerful iterative methods for solving these problems. This book shows its impact on the development of numerical algorithms for problems posed in a function space setting, and is motivated by the idea that a full treatment of a variational problem in function spaces would be incomplete without a discussion of infinite-dimensional analysis, proper discretisation, and the relationship between...

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail.