Applications to ordinary differential equations

Abstract

We will give concrete representation formulas of the approximate solutions for linear ordinary differential equations following the Tikhonov regularization and using a finite number of data. For other applications of reproducing kernels, see a series of papers; for example, [128, 177-181, 232, 233, 283, 284]. In these papers reproducing kernels are applied to nonlinear differential equations using many concrete reproducing kernels with numerical experiments given as well. See also the recent article [477].