REPRODUCING KERNEL FUNCTIONS AND HOMOGENIZING TRANSFORMS - Yildirim, Elif Nuray; Akgul, Ali; İnç, Mustafa (Vinca Inst Nuclear Sci, 2021)
A lot of problems of the physical world can be modeled by non-linear ODE with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution and its effectiveness are as important as the modelling. In this paper, on the basis of reproducing kernel theory, the reproducing kernel functions have been obtained for solving some non-linear higher order differential equations. Additionally, for each problem the homogenizing transforms have been obtained.
Keywords: reproducing kernel functions; PDE; bounded linear operator; hilbert spaces