**Title:** Solutions of high-order linear Volterra integro-differential equations via Lucas polynomials

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-22-00026; **Volume 5 / Issue 1 / Year 2023**, Pages 22-33

**Document Type:** Research Paper

**Author(s):** Deniz Elmacı ^{a} , Nurcan Baykuş Savaşaneril ^{b}

^{a}Dokuz Eylul University, Bergama Vocational School, Izmir, Turkey

^{b}Dokuz Eylul University, Izmir Vocational School, Izmir, Turkey

Received: 15 August 2022, Accepted: 29 November 2022, Published: 28 December 2022

**Corresponding Author:** Deniz Elmacı (Email address: deniz.elmaci@deu.edu.tr)

**Full Text:** PDF

**Abstract**

It is often not possible to find the analytical solution of every type of equation encountered in physics and engineering applications. For this reason, approximate solution methods are needed and errors occur in the solutions obtained by such methods. Therefore, besides being practical and useful, solution methods that give the best approach are sought. For this purpose a matrix method called the Lucas collocation method is presented for numerically solving high-order linear Volterra integro-differential equations under mixed conditions in this paper. Numerical results were compared and interpreted with tables and graphs and the solution was shown to be consistent. The outcomes demonstrate the effectiveness and precision of the current work. On the computer, a MATLAB program was used to run all of the numerical calculations.

**Keywords:** Volterra integro-differential equations, Lucas series and polynomials, Lucas matrix method, collocation points

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