Cubic spline collocation for Volterra integral equations

Authors:
Peeter Oja;Darja Saveljeva
Affiliations:
Institute of Applied Mathematics, Tartu University, Liivi 2, 50409 Tartu, Estonia;Institute of Applied Mathematics, Tartu University, Liivi 2, 50409 Tartu, Estonia
Venue:
Computing
Year:
2002

Citing 3
Cited 4

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Integral equations: theory and numerical treatment
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations

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Stability of collocation by smooth splines for Volterra integral equations

Mathematical Methods for Curves and Surfaces

Convergence of spline collocation for Volterra integral equations

Applied Numerical Mathematics
An algorithm for solving linear Volterra integro-differential equations

Numerical Algorithms
A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations

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Linear/linear rational spline collocation for linear boundary value problems

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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.