Solving Second-Order Delay Differential Equations by Direct Adams-Moulton Method

Abstract

This paper will consider the implementation of fifth-order direct method in the form of Adams-Moulton method for solving directly second-order delay differential equations (DDEs). The proposed direct method approximates the solutions using constant step size. The delay differential equations will be treated in their original forms without being reduced to systems of first-order ordinary differential equations (ODEs). Numerical results are presented to show that the proposed direct method is suitable for solving second-order delay differential equations.

Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations

“…Bartoszewski and Jackiewicz [4] investigate the stability properties of the twostep RK method which any A-stable two-step RK method, the corresponding method is P-stable. Some other authors proposed block linear multistep method (LMM) in solving DDEs and these study can be found in [10]- [30].…”

An efficient method for solving second-order delay differential equation

“…Therefore, it is important to develop effective numerical methods to solve DDEs. In the past two decades, several numerical methods have been proposed for the second order DDEs problem including finite difference method [4,20], two-point block method [18], Adams-Moulton method [19], variational iteration method [15], Legendre-Gauss spectral collocation method [25], initial value method [21].…”

Solving Oscillatory Delay Differential Equations Using Block Hybrid Methods

“…Some authors also derived block linear multistep method (LMM) to solve DDEs; and such work can be seen in [3][4][5][6]. Hoo et al [7] constructed Adams-Moulton Method for directly solving second-order DDEs. Mechee et al [8] in their paper has adapted RKN for directly solving second-order DDEs.…”