Date of Award
Master of Science
Robert M. Corless
This thesis delineates a generally applicable perspective on numerical meth ods for scientific computation called residual-based a posteriori backward er ror analysis, based on the concepts of condition, backward error, and residual, pioneered by Turing and Wilkinson. The basic underpinning of this perspec tive, that a numerical method’s errors should be analyzable in the same terms as physical and modelling errors, is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily in terpretable in the broader context of mathematical modelling. It is applied in this thesis mainly to numerical solution of differential equations. We examine the condition of initial-value problems for ODEs and present a residual-based error control strategy for methods such as Euler’s method, Taylor series meth ods, and Runge-Kutta methods. We also briefly discuss solutions of continuous chaotic problems and stiff problems.
Fillion, Nicolas, "Backward Error Analysis as a Model of Computation for Numerical Methods" (2011). Digitized Theses. 3257.