# Novel symmetric numerical methods for solving symmetric mathematical problems

Ibrahimov, V.R. and Mehdiyeva, G.Y.U. and Yue, Xiao-Guang and Kaabar, Mohammed K.A. and Noeiaghdam, Samad and Juraev, Davron Aslonqulovich (2021) Novel symmetric numerical methods for solving symmetric mathematical problems. International Journal of Circuits, Systems and Signal Processing, 15. pp. 1545-1557. ISSN 1998-4464, DOI https://doi.org/10.46300/9106.2021.15.167.

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## Abstract

—The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p<=8 are constructed to solve some problems, and obtained results are compared with other known methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. On the intersection of multistep and hybrid methods have been constructed multistep methods and have been proved that these methods are more exact than others. And also has been shown that, hybrid methods constructed here are more exact than Gauss methods. Noted that constructed here hybrid methods preserves the properties of the Gauss method. © 2021, North Atlantic University Union NAUN. All rights reserved.

Item Type: Article Hubei ChuTian Scholar Funding, China, Elmin Inkişafı Fondu [Grant No.: EIF-MQM-ETS-2020-1(35)-08/01/1-M-01] Integro-differential equation of Volterra type; Multistep methods of hybrid type; ODE; Symmetric multistep methods; Systems theory and systems engineering; Volterra integral equation; —Initial-value problem Q Science > QA Mathematics Faculty of Science > Institute of Mathematical Sciences Ms Zaharah Ramly 27 Nov 2023 08:06 27 Nov 2023 08:06 http://eprints.um.edu.my/id/eprint/35787