Numerical Solution of Delay Differential Equations via the Reproducing Kernel Hilbert Spaces Method
Reham K. Alshehri
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia.
Banan S. Maayah
Department of Mathematics, Faculty of Science, The University of Jordan, Amman, 11942, Jordan.
Abdelhalim Ebaid *
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
Delay differential equations (DDEs) are generalization of the ordinary differential equation (ODEs), which is suitable for physical system that also depends on the past data. In this paper, the Reproducing Kernel Hilbert Spaces (RKHS) method is applied to approximate the solution of a general form of first, second and third order fractional DDEs (FDDEs). It is a relatively new analytical technique. The analytical and approximate solutions are represented in terms of series in the RKHS.
Keywords: Delay differential equations, reproducing kernel hilbert spaces, approximate solutions.