Guaranteed error bounds for the initial value problem using polytope arithmetic
- 29 Downloads
In this paper we propose and compare modifications of the method of co-ordinate transformations for finding guaranteed bounds for the numerical solution of the initial value problem. These modifications are judged on their success in overcoming exponentially too large growth of the computed error bound.
Key WordsGuaranteed error bounds interval arithmetic co-ordinate transformations polytopes ordinary differential equations
Unable to display preview. Download preview PDF.
- 1.D. P. Davey,Guaranteed bounds on the numerical solutions of initial value problems using polytope arithmetic, Mémoire de maîtrise, Département d'Informatique, Université de Montréal.Google Scholar
- 3.L. W. Jackson,A comparison of ellipsoidal and interval artihmetic error bounds, Numerical Solutions of Nonlinear Problems, Studies in Numerical Analysis, vol. 2, Proc. Fall Meeting of the Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1968.Google Scholar
- 4.L. W. Jackson,Automatic error analysis for the solution of ordinary differential equations, Ph.D. Thesis, Technical Report No. 28, Department of Computer Science, University of Toronto, Toronto, Ontario.Google Scholar
- 5.W. M. Kahan,An ellipsoidal error bound for linear systems of ordinary differential equations, Unpublished manuscript.Google Scholar
- 6.W. M. Kahan,A computable error bound for systems of ordinary differential equations, Abstract in SIAM Review, 8 (1966), pp. 568–569.Google Scholar
- 7.F. Krückeberg,Ordinary differential equations, Topics in Interval Analysis, E. Hansen ed., Oxford University Press, 1969.Google Scholar
- 8.R. E. Moore,Interval arithmetic and automatic error analysis in digital computing, Technical report No. 25, Stanford University Applied Mathematics and Statistics Laboratories, 1962.Google Scholar
- 9.R. E. Moore,Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.Google Scholar
- 10.F. C. Schweppe,Recursive state estimation when observation errors and systems input are bounded, Technical Report, Sperry Rand Research Centre, Sudbury, Massachusetts, 1967.Google Scholar
- 11.N. F. Stewart,A heuristic to reduce the wrapping effect in the numerical solution of x′ = f(t,x), BIT, 11 (1971), pp. 328–337.Google Scholar
- 12.N. F. Stewart,Centrally symmetric convex polyhedra to bound the error in x′ = f(t,x), Abstract in SIAM Review, 14 (1972), p. 213 Available from the author.Google Scholar