Solving Oscillatory Delay Differential Equations Using Block Hybrid Methods

Abstract

A set of order condition for block explicit hybrid method up to order five is presented and, based on the order conditions, two-point block explicit hybrid method of order five for the approximation of special second order delay differential equations is derived. The method is then trigonometrically fitted and used to integrate second-order delay differential equations with oscillatory solutions. The efficiency curves based on the log of maximum errors versus the CPU time taken to do the integration are plotted, which clearly demonstrated the superiority of the trigonometrically fitted block hybrid method.

Second‐Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

“…In CPs, convergence rate R cp is R cp = log ½w apc ðN/2Þ/w apc ðNÞ/log 2: Example 1. Consider DDE of second order [8]…”

“…Chebyshev wavelet technique was developed by Ghasemi and Kajan [7] to solve the DDEs. Ahmad et al [8] solved the DDEs by a block hybrid method. Multistep methods was used by Okunuga and Ehigie [9] to solve the DDEs.…”

Solving Some Oscillatory Problems using Adomian Decomposition Method and Haar Wavelet Method

“…(1) Where is a non-linear operator, L is the highest order derivative which is assumed to be invertible and R is a linear differential operator of order less than . Making subject to formula, we obtain Ly = g x − Ry − Ny (2) By solving (2) for Ly, since L is invertible, we can write…”

“…A new explicit Runge-Kutta method of fifth algebraic order has been developed by Hussain et al for solving second-order ordinary differential equations with oscillatory solutions [1]. A set of order condition for block explicit hybrid method up to order five has been presented for the approximation of special second order delay differential equations with oscillatory solutions [2]. Runge-Kutta methods have been adapted to the numerical integration of oscillatory problems [3].…”

On solving fuzzy delay differential equation using bezier curves

“…Hu et al [8] applied linear multi-step methods to compute numerical solutions for neutral DDEs. Other method obtained approximate solutions for variety of DDEs such as Runge Kutta methods, block methods and one-leg θ-methods in [8][9][10][11][12]. Moreover, the DDEs solved approximately via some approximation methods in many fields of mathematics using approximation methods: for example, the homotopy analysis method [13,14], Adomian decomposition method [15] and homotopy perturbation  ISSN: 2088-8708 Int J Elec & Comp Eng, Vol.…”