Characterization of a next generation step-and-scan system
Timothy J. Wiltshire, Joseph P. Kirk, et al.
SPIE Advanced Lithography 1998
An integration method for ordinary differential equations is said to be contractive if all numerical solutions of the test equation x′=λx generated by that method are not only bounded (as required for stability) but non-increasing. We develop a theory of contractivity for methods applied to stiff and non-stiff, linear and nonlinear problems. This theory leads to the design of a collection of specific contractive Adams-type methods of different orders of accuracy which are optimal with respect to certain measures of accuracy and/or contractivity. Theoretical and numerical results indicate that some of these novel methods are more efficient for solving problems with a lack of smoothness than are the familiar backward differentiation methods. This lack of smoothness may be either inherent in the problem itself, or due to the use of strongly varying integration steps. In solving smooth problems, the efficiency of the low-order contractive methods we propose is approximately the same as that of the corresponding backward differentiation methods. © 1978 BIT Foundations.
Timothy J. Wiltshire, Joseph P. Kirk, et al.
SPIE Advanced Lithography 1998
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
Ziv Bar-Yossef, T.S. Jayram, et al.
Journal of Computer and System Sciences
Corneliu Constantinescu
SPIE Optical Engineering + Applications 2009