Convergence of regularized spline approximants to solutions of initial and boundary value problems for ODE (Q1894385)

For linear initial and boundary value problems for ordinary differential equations (ODEs) spline collocation is a well-known numerical method. This paper deals with the case when the right-hand side of the equation, given on a discrete mesh, includes errors. Following Tikhonov's regularization technique the author investigates the spline approximant as a solution for a minimizing problem. Existence and uniqueness of the solution together with convergence rates are proved. The results are presented for linear initial value problems. A modification for linear boundary value problems with zero boundary condition is possible.