Journal of the Nigerian Mathematical Society

Block Bi-Basis Collocation Method for Direct Approximation of Fourth-order IVP

Blessing Iziegbe Akinnukawe, Mathew Remilekun Odekunle

This study presents the derivation of two-step fifth-order hybrid scheme based on the combination of Hermite and shifted Chebyshev polynomials as bases functions of the collocation techniques. The technique was used to generate a set of hybrid schemes at selected grid and non-grid points and implemented as a block method. The derived block method (Block Bi-basis Collocation Method) was applied as a simultaneous integrator to linear and non-linear fourth-order initial value problems of ordinary differential equations. The zero stability, order, error constants, consistency, convergence and numerical results of the proposed block method are analysed. The application of the block bi-basis collocation method to some fourth-order initial value problems demonstrated the effectiveness and accuracy of the method. The block bi-basis collocation method compared favorably with existing methods in literature.

SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS

Silas Longwap, ABDOUL SALAM DIALLO — Tue, 27 Dec 2022 00:00:00 +0100

A pseudo-Riemannian manifold which admits a field of parallel
null r-planes, with r ≤ n 2 is a Walker n-manifold. A.G. Walker in [12] investi-
gated the canonical forms of the metrics and came out with some interesting re-
sults. Of special interest are the even-dimensional Walker manifolds (n = 2m)
with fields of parallel null planes of half dimension (r = m). In this paper, we
consider a perticular eight-dimensional Walker manifold, derive and investigate
some geometric properties of the curvature tensors of the Manifold. We give
some theorems for the metric to be Einstein and Locally Conformally Flat.

LATTICE POINTS OF DILATIONS OF THE STANDARD 2-SIMPLEX AND THE GRASSMANNIAN Gr(2,n)

Dr. Praise Adeyemo — Tue, 27 Dec 2022 00:00:00 +0100

The connection between the combinatorics of the lattice points of the dilation r∆2 of the standard 2-simplex ∆2 and the cohomology ring of the Grasmmannian Gr(2, r+2) is explored. Specifically, two important refinements of the Ehrhart polynomial
are realized from this connection. One of the refinements interprets the Poincar´epolynomial P(Gr(2, r + 2), z) as the number of lattice points on each of the slicing lines of r∆2 with respect to a fixed weight.

ON THE CONSTRUCTION OF QUANDLES OF ORDER 3N

Abednego Orobosa Isere, Abraham Elakhe, Cletus Ugbolo — Tue, 27 Dec 2022 00:00:00 +0100

We present methods of constructing examples of quandles of order 3n; n > or = 3. The
necessary and sucient conditions for the constructed examples to be (i) connected
(ii) group (conjugate) (iii) involutory and (iv) Alexander quandles are examined and
presented. Two particular examples from these methods are presented for illustra-
tion purpose and their properties are obtained, and these are used in classifying the
constructed examples up to isomorphism.

On the numerical solution of the Kuramoto-Sivashinsky equation using operator-splitting method

Adebayo Abiodun Aderogba, Michael Chapwanya, Jules Djoko Kamdem — Tue, 27 Dec 2022 00:00:00 +0100

An operator-splitting scheme for the Kuramoto-Sivashinsky equation, $u_t+uu_x+u_{xx}+u_{xxxx}=0$, is proposed. The method is based on splitting the convective and the diffusive differential terms thereby permitting an efficient scheme choice for each of them, and when combined give a reliable solution for the entire equation. We demonstrate the accuracy and capability of the proposed split scheme via several numerical experiments. Computations of the bound, $\displaystyle{\limsup_{t\rightarrow \infty}\|u(x,t)\|_2}$ for the equation is also presented.

Stability and Boundedness Analysis of a Prey-Predator System with Predator Cannibalism

Dr. Akinwale Olutimo, Dr. Daniel Adams, Abdullai Abdurasid — Tue, 27 Dec 2022 00:00:00 +0100

The prey-predator system with predator cannibalism is considered in this
papper. We employ the Lyapunov’s direct method for the prey-predator system
and demonstrate its efficacy. This method is built upon theoretical Lyapunov’s
function that is constructed such that the scalar function and its derivative is
positive and negative definite respectively to determine the dynamic behaviour
of the system considered including stability and boundedness. The results show
that the density functions describing the prey-predator system is better rapidly
converging under certain sufficient conditions obtained by the Lyapunov functional.
We give numeric example to support our findings.

Impact of entropy generation on hydromagnetic nanofluid flow dispersed over a radiative vertical porous plate with Newtonian heating

John Omowaye, Olubode Koriko — Tue, 27 Dec 2022 00:00:00 +0100

Recently and over the years, the industrial applications of second law analysis is becoming famous. Hence, this work intend to address the combined impacts of water-based nanofluids, convective boundary state, thermal radiation, magnetic field and second law of thermodynamics .The governing equations that unravel the flow within the boundary layer are provided. The transformed governing equations are obtained by guided similarity variables, the transformed equations are solved analytically by method of undetermined coefficient. Entropy generation rate and Bejan number in dimensionless form are obtained by deriving an expression through the analytical solutions of temperature and velocity. The emerging parameters of the flow are: Bejan number, Biot number, radiation parameter, entropy generation rate, skin friction, Hartman number, suction, Prandtl, Nusselt and Reynolds number. Also, the effects of these parameters are presented in graphs and tables. In addition, Entropy generation are enhanced by Eckert number, radiation parameter, permeability parameter, suction , prandtl number and Brinkman number for both copper and alumina water. Finally, the results of this work is compared with published work in the literature, this result is in consonant with this work.

ON INDEPENDENCE POLYNOMIALS OF QUOTIENT BASED GRAPHS FOR FINITE ABELIAN GROUPS

Aliyu Suleiman, A.I . Kiri — Tue, 27 Dec 2022 00:00:00 +0100

In this paper we investigated the independence polynomial of quotient based graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ of an abelian group $G$ relative to all it's subgroups since a subgroup $H$ of an abelian group is normal . The graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ is a graph with condition of adjacency where two distinct elements $x,y \in G$ are adjacent in the graph iff $xy \notin H$. A formula for computing the independence polynomial is obtained.