Convergence of regularized spline approximants to solutions of initial and boundary value problems for ODE
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.
scientific article; zbMATH DE number 777853
scientific article