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Original Articles

The numerical solution of higher index differential–algebraic equations by 4-point spline collocation methods

Pages 1299-1312 | Received 06 Feb 2001, Accepted 08 Apr 2002, Published online: 12 May 2010
 

Abstract

We study the order, stability, and convergence properties of 4-point spline collocation methods if applied to differential/algebraic systems with index greater than or equal one. These methods do not in general attain the same order of accuracy for higher index differential/algebraic systems as they do for index-1 systems and for purely differential systems. We show that the 4-point spline collocation methods applied to differential/algebraic systems with index-ν are stable and the order of convergence is 8 − ν, ν = 2(1)7. For both index-1 and purely differential systems the order is seven. Finally, some numerical experiments are presented that illustrate the theoretical results.

Acknowledgements

The authors are indebted to Professor S. E. El. Gendi for various valuable suggestions and constructive criticism

Notes

*On leave from Department of Mathematics, Faculty of Science, Teshreen University, Latakia, Syria

Additional information

Notes on contributors

S. M. MahmoudFootnote*

*On leave from Department of Mathematics, Faculty of Science, Teshreen University, Latakia, Syria

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