http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7192 JAEM 2026, Vol 16, No 3 koleksiyonunu içerir. 2026-04-14T21:29:40Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7202 Investigation of the Conjugate gradient methods in solving the unconstrained nonlinear optimization problem and its applications Shakir, Amel Nashat; Taha, Forat Mohammed In this paper, we consider various types of methods such as; Newton, QuasiNewton, Conjugate gradient, Trust region algorithm and etc. to solve an unconstrained nonlinear optimization problem. in most practical applications, the conjugate gradient method is the most efficient method to solve the large-scale optimization problems. Numerical experimants show that, the conjugate gradient method requires less storage memory compared to that of existing ones. In this paper, we describe the solution of monotone nonlinear equations systems using the conjugate gradient methods. 2026-03-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7201 Newly developed single-step block method for numerical solution of fourth order ordinary differential equations Adebiyi, Adebayo Femi; Udoye, Adaobi Mmachukwu; Akinola, Lukman Shina; Mathew, David Adeleke This paper focuses on the development of a new block method for solving fourth order initial value problems of ordinary differential equations. Applying Chebyshev polynomial as a basis function, the method was developed using interpolation and collocation approaches. The convergence property of the method was established with zero-stability and consistency. Comparison was made with existing method, and the newly developed method compares favourably well. 2026-03-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7200 Inverse and connected domination in Hypertree Networks Shalini, V.; Rajasingh, Indra A dominating set of a graph G = (V, E) is a subset D of vertices such that every vertex in V \ D is adjacent to at least one vertex in D, and the minimum size of such a set is called the domination number denoted by γ(G). If D is a minimum dominating set of G and there exists a dominating set D′ within V \ D, then D′ is called an inverse dominating set with respect to D. The minimum cardinality of such a set is known as the inverse domination number, denoted by γ′ (G). A dominating set D is called a connected dominating set if the induced subgraph ⟨D⟩ is connected in G. The minimum cardinality of a connected dominating set is called the connected domination number, denoted by γc(G). In this paper, we have computed the inverse and connected domination numbers for Hypertree Networks. 2026-03-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7199 Injective coloring of central graphs Mirdamad, Shahrzad Sadat; Mojdeh, Doost Ali For a given graph G = (V (G), E(G)), researchers have introduced different colorings based on the distances of the vertices. An injective coloring of a graph G is an assignment of colors to the vertices of G such that no two vertices with a common neighbor receive the same color. The injective chromatic number of G, denoted by χi(G), is the minimum number of colors required for an injective coloring of G. The concept of a central graph of any graph has been a widely studied topic among mathematical researchers and graph theorists nowadays. The central graph of a given graph G, denoted by C(G), is the graph obtained by subdividing each edge of G exactly once and also adding an edge between each pair of non-adjacent vertices of G. In this work, we present some results on injective coloring of central graph C(G) of G. We show that for a graph G of order n and maximum degree ∆(G), n − 1 ≤ χi(C(G)) ≤ n² − 3n − (n − 3)∆(G) + 3. Next, we will closely examine the injective chromatic number of the central graph of some special graphs and trees. Finally, for any graph H, and the corona product (H ◦ K1), (H ◦ K2), we will have a precise determination of the injective chromatic number of C(H ◦ K1) and C(H ◦ K2) in terms of χi(C(H)) and order of H. 2026-03-01T00:00:00Z