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

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.

Keywords:

• Differential/algebraic equations
• Spline collocation methods
• Higher index

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. Mahmoud*

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