Quadratic spline collocation for Volterra integral equations
In the traditional one-step collocation method in the space of \(C^1\)-quadratic splines for second-kind Volterra integral equations, the authors replace one of the required initial conditions by a ``not-a-knot'' boundary condition at the right endpoint of the interval of integration. This nonlocal method yields uniform boundedness of the collocation projection for all collocation parameters \(c\in(0, 1)\). For \(c= 1\) the projection norms exhibit linear growth, and hence for any choice of c appropriate general convergence theorems can be used to establish the convergence based on two-sided error estimates. Numerical illustrations for linear problems with constant (positive or negative) kernels confirm the foregoing analysis.
scientific article; zbMATH DE number 2155013
scientific article