Abstract
This study aims to solve the renewal delay integro-differential equations constrained by the half-line, introducing a computational method composed of the matrix relations of the Stieltjes–Wigert polynomials at the collocation points. In order to mathematically interpret their robust integral part, the method is also fed neurally by the Stieltjes–Wigert polynomials and a hybrid polynomial dependent upon the alteration of the Taylor and exponential polynomial bases. Thus, the method easily gathers the matrix relations into a matrix equation and immediately produces a desired solution. An error bound analysis is established to discuss the accuracy of the method by employing the collaboration of the mentioned polynomials. A population model with time-lags (delays), the detection of the displaced atoms versus kinetic energy, an integral delay equation, and a delayed problem with functional kernel are firstly treated by the method. Consequently, it is evident that the method presents a novel consistent approach and is directly programmable on a mathematical software thanks to its neural structure.
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Kürkçü, Ö.K. A neural computational method for solving renewal delay integro-differential equations constrained by the half-line. Math Sci (2022). https://doi.org/10.1007/s40096-022-00492-y
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DOI: https://doi.org/10.1007/s40096-022-00492-y