A Nodal Spline Collocation Method for Weakly Singular Volterra Integral Equations
نویسندگان
چکیده
A collocation method based on optimal nodal splines is presented for the numerical solution of linear Volterra integral equations of the second kind with weakly singular kernel. Since the considered spline operator is a bounded projector we can prove that, for sequences of locally uniform meshes, the approximate solution error converges to zero at exactly the same optimal rate as the spline approximation error. We consider in particular sequences of graded meshes, for which the local uniformity is proved. Finally, we give an upper bound for the condition number of the collocation system and we present some numerical examples.
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