10.1007/s40096-021-00388-3

A numerical scheme for the solution of neutral integro-differential equations including variable delay

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  • Burcu Gürbüz*1,
  1. Johannes Gutenberg - University of Mainz, Mainz, DE Institute of Mathematics, Johannes Gutenberg-University Mainz, İMainz, DE
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Published in Issue 2021-03-13

How to Cite

Gürbüz, B. (2021). A numerical scheme for the solution of neutral integro-differential equations including variable delay. Mathematical Sciences, 16(1 (March 2022). https://doi.org/10.1007/s40096-021-00388-3
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Abstract

Abstract In this study, an effective numerical technique has been introduced for finding the solutions of the first-order integro-differential equations including neutral terms with variable delays. The problem has been defined by using the neutral integro-differential equations with initial value. Then, an alternative numerical method has been introduced for solving these type of problems. The method is expressed by fundamental matrices, Laguerre polynomials with their matrix forms. Besides, the solution has been obtained by using the collocation points with regard to the reduced system of algebraic equations and Laguerre series.

Keywords

  • Neutral type equations,
  • Integro-differential equation,
  • Variable delays,
  • Laguerre polynomial and series,
  • Matrix method
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