Analytical Algorithm for Systems of Neutral Delay Differential Equations

Abstract

Delay differential equations (DDEs), as well as neutral delay differential equations (NDDEs), are often used as a fundamental tool to model problems arising from various areas of sciences and engineering. However, NDDEs particularly the systems of these equations are special transcendental in nature; it has therefore, become a challenging task or times almost impossible to obtain a convergent approximate analytical solution of such equation. Therefore, this study introduced an analytical method to obtain solution of linear and nonlinear systems of NDDEs. The proposed technique is a combination of Homotopy analysis method (HAM) and natural transform method, and the He's polynomial is modified to compute the series of nonlinear terms. The presented technique gives solution in a series form which converges to the exact solution or approximate solution. The convergence analysis and the maximum estimated error of the approach are also given. Some illustrative examples are given, and comparison for the accuracy of the results obtained is made with the existing ones as well as the exact solutions. The results reveal the reliability and efficiency of the method in solving systems of NDDEs and can also be used in various types of linear and nonlinear problems.

Solving neutral delay differential equations using least square method based on successive integration technique

“…The solution graphs obtained by using the proposed CLSM and DLSM with N = 7 are compared with Analytical algorithm presented in [20]. They are given in Figure 2.…”

A Efficient Analytical Approach for Nonlinear System of Advanced Lorenz Model

“…In this research, an efficient analytical approach is applied to solve a model from mathematical physics namely the Advanced Lorenz system. This approach is developed in [4] for an efficient analytical approximation of different forms of the systems of nonlinear retarded delay differential equations (RDDEs). Therefore, the aim here is to find a better approximation analytically of this model using the proposed technique.…”

“…The present work focus to obtain a better analytical approximation for Advanced Lorenz system model by using the approach developed in [4] for the systems of nonlinear RDDEs. This technique is from the combinational form of Natural transform (NT) and Homotopy analysis method (HAM) where the modification of He's polynomial is successfully derived for the computions of nonlinear functions.…”

“…To find the approximation for the system in Eq. (1) based on the proposed technique, The NT of Equation should be first taking, and then by making the further simplification using the given initial condition the simplified form of the model is obtained as So, by following the procedure in [4] the recursive relation of the model can be obtained as…”