Solution of Delay Differential Equations Using a Modified Power Series Method

Abstract

This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this new approach is applicable to both linear and nonlinear problems. The method produces a system of algebraic equations which is solved to determine the coefficients in the trial solution. The method provides the solution in form of a rapid convergent series. The obtained results for numerical examples demonstrate the reliability and efficiency of the method.

On the numerical solution of second order delay differential equations via a novel approach

“…Sedaghat et al [27], developed a numerical method based on Chebyshev polynomials to study the approximate solution of DDEs. Ogunlaran and Olagunju [23] solved the DDEs by using the modified power series method. Senu et al [28], studied the numerical solution of the DDEs using the two-derivative RKM with Newton interpolation.…”

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

“…Recently, DDEs have received considerable attention and have proven to model many real life problems accurately. Researchers used several numerical methods to solve such problems such as Runge-Kutta methods [3,4], linear multi-step methods [21], Adomian decomposition method [8], perturbation-iteration algorithms [15], homotopy analysis method [1], homotopy perturbation methods [17], iterative decomposition method [14], power series [12], block methods [13] and variational iteration method [18].…”