Defect Minimization in Operator Equations: Theory and Applications (Pitman Research Notes in Mathematics Series)

ABOUT THIS VOLUME. This Research Note is devoted to the method of 'defect minimization', a technique which has been shown to yield highly accurate numerical solutions for a variety of problems.In the first part of the book, a general theoretical framework for this method is developed. In the second part, the theoretical results are used to analyse the method in some special cases. The examples treated are some boundary value problems for ordinary differential equations, the classical direct Stefan problem (a well-posed problem for the heat equation), and the inverse Stefan problem (a related ill-posed problem). Computable error bounds for the temperature and the free boundary in the classical Stefan problem are provided in an appendix. Researchers and graduate students in approximation, optimization, numerical analysis and engineering.