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