Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation

Abstract

In this research, a new approach is presented for solving delay differential equations (DDEs) which is a blend of Sumudu transform and variational iteration method (VIM). A general Lagrange multiplier is used to construct a correction functional. This is done with an uncommon Sumudu transform alongside variational theory. A few numerical cases were solved to demonstrate methodology of this new approach. Objective of this research is to reduce the complexity of computational work compared to the conventional approaches. It can be concluded that the amount of evaluation is reduced but at the same time the results are comparable as in the previous works.

Application of the alternative variational iteration method to solve delay differential equations

“…Which is closed form to the exact solution and the results due to Biala et al (2014) and Vilu et al (2019) and Alomari et al (2009). The solution behavior of () Figure 3.…”

“…In this paper, AVIM has been applied for finding the Figure 6. Plots of the absolute errors for some values of t with SVIM [Vilu et al (2019)] and AVIM in Example 3. approximate solutions of the linear and nonlinear DDE. The method gives more realistic series solutions that converge quickly in physical problems.…”

“…In this part, three examples are provided that illustrate the method of Biala et al 2014, Vilu et al (2019), Alomari et al (2009).…”

“…Subsequent Batiha et al (2007), Mahdy et al (2015), Noor and Mohyu-Din (2008), Wazwaz (2009) and Wu (2013) reflect the VIM procedure's versatilliy, reliability and performance. The aim of this paper is to use alternative method of variational iteration (AVIM) (Sakar and Ergoren, 2015;Singh and Kumar, 2017) to solve linear and nonlinear differential equations of delay (Biala et al, 2014;Vilu et al, 2019;Alomari et al, 2009). We show that by standard of variational iteration the approximate solution thus obtained converges more easily relative to the approximate solutions.…”

“…In disparate ordinary differential equation (ODE), where the initial conditions are defined at preliminary point, DDEs given device history as the initial conditions over the delay interval. Different kinds of vigorous techniques have been developed in recent years to find an approximate solution for these such delay differential equations, as the Sumudu variational iteration method (SVIM) Vilu et al (2019), the Laplace variational iteration method (LVIM) Biala et al (2014), the Optimal homotopy asymptotic method (OHAM) Anakira et al (2013), the Differential transform method (DTM) Karakoc and Bereketoglu (2009), Rashidi et al (2011), the Homotopy perturbation method (HPM) Shakeri and Dehghan (2008), the Adomian decomposition method (ADM) Evans and Raslan (2007) and the Homotopy analysis method (HAM) Alomari et al (2009), Hassan and Rashidi (2011). The method of variational iteration method (VIM) was developed for solving nonlinear problems by He (1999He ( , 2000He ( , 2004He ( , 2007 He and Wang (2007) and He and Wu (2007).…”