Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2004-12-31
Quadratic Spline Collocation for Volterra Integral EquationPeeter Oja and Darja Saveljeva (1) Tartu University, Estonia
(2) Tartu University, Estonia
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.
Keywords: Quadratic spline collocation, spline projections, Volterra integral equations, stability and convergence of spline collocation method
Oja Peeter, Saveljeva Darja: Quadratic Spline Collocation for Volterra Integral Equation. Z. Anal. Anwend. 23 (2004), 833-854. doi: 10.4171/ZAA/1227