Spline Approximation and Difference Schemes for the Heat Equation

摘要

It is proved that the spline approximation by Galerkin's method of the solution of the initial-value problem for the heat equation can be considered as the successive application of an associated finite difference operator and a spline interpolation operator. If the splines considered are of order mu, the finite difference operator is parabolic and accurate of order 2mu - 2. Some consequences of this fact are discussed. (Author)