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The numerical solution of ordinary and algebraic differential equations using one step methods

Keogh, Gerard (1990) The numerical solution of ordinary and algebraic differential equations using one step methods. Master of Science thesis, Dublin City University.

This thesis addresses the problem of finding numerical solutions to ordinary and algebraic differential equation systems. Our primary focus is the application of onestep numerical schemes to these problem classes. Firstly we concentrate on the narrower class of explicit Ordinary Differential Equation (O DE) systems. We analyse the theory necessary develop efficient algorithms based on our chosen one-step numerical schemes. These algorithms are then applied to the solution of a standard test set of ODE systems. The results are then compared with those obtained using standard software packages on the same problem test set. Our theory is then extended to include the wider class of Algebraic Differential Equation (more commonly called Differential Algebraic Equation (D A E ) ) systems. Based on this theory, we are able to adapt our one-step schemes to solve this harder class of problem. Once again the resulting algorithms are tested on a selection of problems and results are compared with those obtained from standard software packages. On all problems considered, we demonstrate that our techniques can often provide efficient alternatives to the more complex methods adopted in the standard software packages designed for these problem classes.
Item Type:Thesis (Master of Science)
Date of Award:1990
Supervisor(s):Carroll, John
Uncontrolled Keywords:Numerical solutions; Ordinary differential equations; Differential algebraic equations
Subjects:Mathematics > Algebra
Mathematics > Differential equations
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:18933
Deposited On:22 Aug 2013 13:45 by Celine Campbell . Last Modified 22 Aug 2013 13:45

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