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Improving the Efficiency of Runge-Kutta Methods for the Solution of BVPs for Higher-Order ODEs (1996)
BibTeX
@MISC{Odes96improvingthe,
author = {Bvps For Higher-order Odes and Khalid Zuberi and Khalid Zuberi},
title = {Improving the Efficiency of Runge-Kutta Methods for the Solution of BVPs for Higher-Order ODEs},
year = {1996}
}
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Abstract
Improving the Efficiency of Runge-Kutta Methods for the Solution of BVPs for Higher-Order ODEs Khalid Zuberi Master of Science Graduate Department of Computer Science University of Toronto, 1996 Runge-Kutta methods are often used to solve two-point boundary value problems (BVPs) for ordinary differential equations (ODEs.) These methods are usually applied directly to first-order systems; to solve problems for higher-order ODEs, the differential equations are often reduced to an equivalent first-order system. We exploit the structure of the reduced system to construct an approximate Jacobian matrix that is significantly cheaper to construct for general higher order BVPs. Second-order ODEs are examined in detail, and a specialised linear system solver is suggested to provide additional computational savings. Numerical results on sample BVPs for second-order ODEs show significant computational savings with no loss of solution accuracy. ii Acknowledgements I would like to thank m...
Keyphrases
runge-kutta method higher-order ode computer science university science graduate department higher-order ode khalid zuberi master two-point boundary value problem solution accuracy ordinary differential equation numerical result ii acknowledgement equivalent first-order system sample bvps approximate jacobian matrix order bvps second-order ode first-order system additional computational saving linear system solver differential equation reduced system
