JournalszaaVol. 23, No. 4pp. 833–854

Quadratic Spline Collocation for Volterra Integral Equation

  • Peeter Oja

    Tartu University, Estonia
  • Darja Saveljeva

    Tartu University, Estonia
Quadratic Spline Collocation for Volterra Integral Equation cover

Abstract

In the traditional step-by-step collocation method with quadratic splines 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 nonlocal method gives the uniform boundedness of collocation projections for all parameters c in (0,1) characterizing the position of collocation points between spline knots. For c = 1 the projection norms have linear growth and, therefore, for any choice of c some general convergence theorems may be applied to establish the convergence with two-sided error estimates. The numerical tests supporting the theoretical results are also presented.

Cite this article

Peeter Oja, Darja Saveljeva, Quadratic Spline Collocation for Volterra Integral Equation. Z. Anal. Anwend. 23 (2004), no. 4, pp. 833–854

DOI 10.4171/ZAA/1227