A Numerical Method by Reproducing-Kernel Approximation for the Pantograph Equation M.I. Syam, H.M. Jaradat, M. Alquran

Abstract

In this paper, we study the pantograph equation. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniform convergent of the proposed method is investigated.