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Saghir Ahmad

Doctor of Philosophy, (Mathematics)
Study Completed: 2016
College of Sciences

Citation

Thesis Title
Design and construction of software for general linear methods

Read article at Massey Research Online: MRO icon

In the field of numerical analysis implementation of methods for solving ordinary differential equations arise in many branches of science and engineering. Mr Ahmad investigated the use of an efficient class of general linear methods to develop robust algorithms. His research involved designing a numerical process which, as much as possible, avoided ad hoc, heuristic and empirical design features which are common in existing software. For adaptability to specific problems and numerical behaviour, variable mesh size and variable order are required. In addition, decisions need to be made dynamically about acceptance or possible rejection of steps as they are performed. Using a novel approach (Lagrange optimisation) Mr Ahmad successfully balanced the needs of accuracy and efficiency while avoiding the use of several heuristic choices. His research gives a new direction for developing reliable software.

Supervisors
Professor John Butcher
Associate Professor Winston Sweatman