Semianalytical Approach for the Approximate Solution of Delay Differential Equations

Abstract

In this analysis, we develop a new approach to investigate the semianalytical solution of the delay differential equations. Mohand transform coupled with the homotopy perturbation method is called Mohand homotopy perturbation transform method (MHPTM) and performs the solution results in the form of series. The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. Some illustrated examples are interpreted to confirm the accuracy of the newly developed scheme.

A Numerical Approach for the Analytical Solution of the Fourth-Order Parabolic Partial Differential Equations

“…Put Equations ( 24)- (26) in Equation ( 22), and comparing the similar factors of p, we get the following consecutive elements:…”

“…Nadeem et al [13] applied the Laplace transform coupled with the homotopy perturbation method to solve the fourth-order parabolic PDEs with variable coefficients. Luo et al [26] introduced a combined form of the Mohand transform and the homotopy perturbation method to provide the analytical solution of the delay differential equations. Recently, many integral transformations have been introduced to find the approximate solution of ordinary and partial differential equations such as the Elzaki transform [27,28], Sumudu transform [29], Aboodh trans-formation [30], Mohand transform [31], and homotopy perturbation method [24].…”

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

“…Additionally, the author combined the generated schemes and their derivatives to create block techniques, which enable the simultaneous direct solution of second-order DDEs without the laborious requirement of building separate predictors. To analyze the semianalytical solution of the DDEs, the writers of the effort [17] construct a novel technique called the Mohand homotopy perturbation transform method (MHPTM). This approach combines the Mohand transform with the homotopy perturbation method (HPTM).…”

“…Several intellectuals have created a variety of analytical integral transform techniques for precise and approximated answers during the past few years, including the Laplace transform method [25,26], Shehu transform method [27,28], Aboodh transform method [22], Sumudu transform method [29], Elzaki transform method [30], and Mohand transform method [17]. The Sumudu transform method is an integral like the Laplace transform method, introduced in the early 1990s by Watugala [31] to solve DEs and control engineering problems.…”

“…The author of the study [29] successfully integrated the double Sumudu transform with the iterative approach to produce an approximate analytical answer to the one-dimensional coupled NLSGE, which cannot be solved by utilizing the double Sumudu transform alone. In this approach, the linear part of the problem was handled [17,22,36].…”