A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

TL;DR

This paper introduces a polynomial collocation method for numerically solving retarded functional differential equations, providing error analysis and demonstrating accuracy through illustrative examples relevant to science and engineering applications.

Contribution

It presents a novel polynomial collocation approach for retarded functional differential equations with error analysis, enhancing numerical solution techniques.

Findings

Method achieves high accuracy in examples

Error bounds are established for the approximation

Applicable to various science and engineering models

Abstract

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.