Research Article
A Meshless Method for Solving 1D Heat Equation on a Semicircle
Aguemon Wiwegnon Uriel-Longin*,
Kalivogui Siba,
Tchiekre Michel Henri Daugny,
Badiane Marcel Sihintoe,
Coulibaly Bakary D,
Bah Thierno Mamadou
Issue:
Volume 15, Issue 2, April 2026
Pages:
49-59
Received:
4 November 2025
Accepted:
1 December 2025
Published:
18 March 2026
Abstract: In this work, we present the one-dimensional heat equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on R2. The basis of approximation used for this paper, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines curves. We calculate the numerical solution of the heat equation using the principle of Galerkinโs method. The numerical solution is calculated, using the parametrization of the domain and using the numerical integration of Gauss. Solving this partial differential equation leads to solving a system of differential equations. This system will be solved using the classic fourth-order Runge-Kutta method and a CFL condition. Numerical tests have been presented to show the efficiency of this method.
Abstract: In this work, we present the one-dimensional heat equation solving by the isogeometric method, a meshless method using Galerkin Method. This equation has been solved on a semicircle, a curve on R2. The basis of approximation used for this paper, is the B-splines basis. We define univariate B-splines. We look at their properties as well as b-splines...
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Research Article
On Weakly S-Prime Ideal Graph Of a Finite Commutative Ring
Kalamani Duraisamy
,
Vasuki Shanmugam*
Issue:
Volume 15, Issue 2, April 2026
Pages:
60-67
Received:
26 February 2026
Accepted:
28 March 2026
Published:
24 April 2026
DOI:
10.11648/j.acm.20261502.12
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Abstract: Let โ be a finite commutative ring with unity. Let โ be a proper ideal of โ and ๐ฎ is the multiplicative closed subset of โ which is disjoint with โ. The weakly S-prime ideal graph denoted by Gโ(โ) is the undirected graph whose vertex set is the set of elements ๐ข of โ such that the non-zero product ef is in โ and either se is in โ or sf is in โ for some f in โ and the two distinct vertices ๐ข and ๐ฃ are connected by an edge if and only if either se is in โ or sf is in โ for some s in ๐ฎ. The purpose of this article is to investigate the graph theoretic properties of the weakly S-prime ideal graph associated with โ. This study focuses on rings of order 2๐ญ, 3๐ญ and ๐ญ๐ฎ, where ๐ญ and ๐ฎ are distinct primes. For these rings, the weakly S-prime ideal graph is a special type of graph and it is explained with examples. Furthermore, the graph theoretic concept of the weakly S-prime ideal graph Gโ(โ) namely its girth, diameter, radius and size are studied. The relation between the weakly S-prime ideal graph and annihilator ideal graph associated with a ring of order 2๐ญ is described and it is proved that these two graphs are isomorphic.
Abstract: Let โ be a finite commutative ring with unity. Let โ be a proper ideal of โ and ๐ฎ is the multiplicative closed subset of โ which is disjoint with โ. The weakly S-prime ideal graph denoted by Gโ(โ) is the undirected graph whose vertex set is the set of elements ๐ข of โ such that the non-zero product ef is in โ and either se is in โ or sf is in โ fo...
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