Computing

, Volume 69, Issue 4, pp 319–337 | Cite as

Cubic Spline Collocation for Volterra Integral Equations

  • Peeter Oja
  • Darja Saveljeva

Abstract

In the standard step-by-step cubic spline collocation method for Volterra integral equations an initial condition is replaced by a not-a-knot boundary condition at the other end of the interval. Such a method is stable in the same region of collocation parameter as in the step-by-step implementation with linear splines. The results about stability and convergence are based on the uniform boundedness of corresponding cubic spline interpolation projections. The numerical tests given at the end completely support the theoretical analysis.

AMS Subject Classification: 65D07, 65R20, 41A15. 
Keywords: cubic spline collocation, spline projections, Volterra integral equations, stability and convergence of spline collocation method. 

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Peeter Oja
    • 1
  • Darja Saveljeva
    • 2
  1. 1.Institute of Applied Mathematics Tartu University Liivi 2 50409 Tartu Estonia e-mail: peeter_o@ut.eeEE
  2. 2.Institute of Applied Mathematics Tartu University Liivi 2 50409 Tartu Estonia e-mail: darja@ut.eeEE

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