In this article, we report a combined concept of linearties and nonlinearties of homotopy perturbation method using Laplace transform with He’s polynomials for solving complex delay differential equations which have a versatile application in signal processing, digital image processing, physics and applied sciences. Some examples are given to illustrate the ability and reliability of the proposed method, and the results are compared with VIM and exact solution after taking sum of first four iterations of approximate solution. Convergence analysis is discussed after implementing Banach fixed point theorem.

中文翻译：

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带有Laplace变换的He's多项式的时滞微分方程的同伦摄动方法

在本文中，我们报告了使用Laplace变换和He多项式求解同构摄动方法的线性和非线性的组合概念，用于求解复杂的延迟微分方程，这些方程在信号处理，数字图像处理，物理学和应用科学中具有广泛的应用。给出了一些例子来说明该方法的能力和可靠性，并在对近似解的前四次迭代求和后，将结果与VIM和精确解进行了比较。实施Banach不动点定理后，讨论了收敛性分析。