Date of Award


Degree Type


Degree Name

Master of Science


Applied Mathematics


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.



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