Approximate Solutions of Multi-Pantograph Type Delay Differential Equations Using Multistage Optimal Homotopy Asymptotic Method

Abstract

In this paper, a numerical procedure called multistage optimal homotopy asymptotic method (MOHAM) is introduced to solve multipantograph equations with time delay. It was shown that the MOHAM algorithm rapidly provides accurate convergent approximate solutions of the exact solution using only one term. A comparative study between the proposed method, the homotopy perturbation method (HPM) and the Taylor matrix method are presented. The obtained results revealed that the method is of higher accuracy, effective and easy to use.

Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation

“…In recent years, especially, for several decades, applications of powerful tools for solving numerical and analytical cases have attracted attentions of scientists from all over the world [1]. Delay differential equations (DDEs) are a kind of functional differential equation having a widespread range of uses in the arena of science, technology, and engineering which acquires numerical/analytical solutions.…”

Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models

“…The pantograph differential equations have many applications in the area of theory [2], cell-growth biological based models [3] and control system [4]. The pantograph differential equations have been solved by many techniques, some of them are intelligent networks [5], Chebyshev spectral scheme [6], spectral tau scheme [7], multidimensional homotopy optimal asymptotic scheme [8], Genocchi operational based matrix scheme [9], least-squares-Epsilon-Ritz scheme [10], Taylor operation scheme [11], Galerkin multi-wavelets scheme [12], heuristic computing approach [13], Sinc numerical scheme [14], Laplace transform scheme [15], spectral collocation approach [16], multistep block method [17], Legendre Tau computational scheme [18] and Euler-Maruyama scheme [19]. This singular study is considered very significant due to its extensive applications in radiators cooling, dusty fluids, classical/quantum-based mechanics, models of gas cloud and galaxies [20][21][22].…”

Optimal Type-3 Fuzzy System for Solving Singular Multi-Pantograph Equations

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