时滞泛函微分方程解的计算近似及其在科学和工程中的应用
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
摘要：
时滞微分方程在科学、工程、医学和生物模型中有着重要的应用。这类模型中包含了时滞现象，这对机器学习、力学、经济学、电动力学等领域的实际应用有很大的帮助。此外，一些特殊类型的泛函微分方程也得到了广泛的研究。在这项研究中，这些模型的延迟类型的数值研究连同初始条件。该技术是基于一个多项式的方法以及配置点，保持一个近似的解决方案的问题。此外，还给出了近似解的误差分析。结果表明了该方法的准确性。因此，说明性的例子被认为是获得问题的详细分析。最后，对未来的发展前景进行了展望。
英文摘要：
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Besides, an error analysis of the approximate solutions is given. Accuracy of the method is shown by the results. Consequently, illustrative examples are considered and detailed analysis of the problem is acquired. Consequently, the future outlook is discussed in conclusion.
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