Application of minimal interpolation splines to solve the Cauchy problem (Q946028)

The classical Adams method for the numerical solution of an initial value problem for an ordinary differential equation consists of rewriting the problem as an equivalent Volterra equation, then replacing the integrand by an interpolating polynomial and finally integrating this polynomial exactly to compute the required approximate solution. The authors of the paper under review suggest to replace the interpolating polynomial in this construction by a spline function that satisfies an Hermite interpolation condition. The other parts of the algorithm remain unchanged. A numerical example is given but there is no theoretical investigation of the modified scheme with respect to properties like convergence, consistency or stability.