Espaços de reprodução e aproximação de soluções de equações funcionais

Abstract

The objective of this work is to present, implement and propose numerical reproducing kernel methods to linear and non-linear functional equations, like differential and integral ones. We also have presented a brief introduction to positive definite kernels and reproducing kernel Hilbert spaces theory, and some projection methods to functional equations. We provide a new proposal for the methods of reproduction spaces which dispenses the use of the inner product of the space. Numerical simulations generated good results and the implemented R-language codes are available at the appendix of this work. Finally, we discuss the results obtained.