A block method for solving second order pantograph equation arising in a cell growth model

In this paper we present a block method to solve the second order pantograph equation. The functional equation comes from a cell growth model based on the Fokker-Planck equation. We convert the pantograph equation to an integral equation, then we solve the integral equation by a block method based on the Romberg quadrature rule. Also, we undertake the convergence analysis and finally we show efficiency and validity of the proposed method by numerical examples.