Journal of the Nigerian Mathematical Society

TWO-STEP RUNGE-KUTTA METHODS FOR THE NUMERICAL INTEGRATION OF NONLINEAR SINGULAR AND SINGULARLY PERTURBED IVPs

2024-12-09T02:31:05+01:00

We construct stable Runge-Kutta methods with fewer function evaluations per step by using the two end points of the integration interval as collocation points in addition to the Gaussian interior collocation points. As a result, the methods' rate of convergence is quite high. The advantage of these methods as compared, for example, with methods of the conventional type (Gauss, Radau and Lobatto Runge-Kutta methods) consists of the fact that they provide uniform approximations of the solution of singularly perturbed systems in ordinary differential equations (ODEs), over the entire integration interval. This is in contrast to the conventional Runge-Kutta methods for which the continuous approximation to the exact solution of ODEs is obtained at the mesh points only. Although the computational cost of these methods is little more than the explicit methods, the advantages gained such as high orders, improved regions of absolute stability and lower error constants, make the methods suitable for solving stable systems. By demonstrating two potential implementations of the collocation methods, the desired goal of the derivation is achieved. Results obtained are presented in Tables, while graphic surface curves are shown in Figures to illustrate the accuracy and effectiveness of the derived methods.

A NUMERICAL SOLUTION OF EYRING-POWELL MHD NANOFLUID FLOW WITH CONVECTIVE SURFACE CONDITION AND DUFOUR-SORET IMPACT PAST A VERTICAL PLATE

2025-01-06T17:08:00+01:00

Application of fluid model rely greatly on the fundamental knowledge of pertinent fluid parameter and their significant in decision making in industries and engineering. To this end, utilizing a good method to ascertain some of these importance is needed. In this study the Runge-Kutta-Fehlberg Method is employed to solve numerically the transformed nonlinear ordinary differential equation obtain via some suitable similarity transformation. The computational analysis is presented through graphs for some pertinent parameters. The result shows the combine effect of Soret-Dufour effect on temperature and concentration profile but no significant effect on the velocity. The obtained result under some limiting condition were in good agreement with already established result in the literature.

SENSITIVITY ANALYSIS OF ZIKA VIRUS DISEASE AND CONTROL BY WOLBACHIA-JNFECTED AEDES AEGYPT MOSQUITOES

2024-09-20T00:00:03+01:00

Sensitivity analysis of parameters contained in the reproduction number of an infectious disease, helps to reveal how the parameters of the disease dynamics impact on the spread of the disease, and in that case, suggest appropriate method of control for the disease. The aim of this paper is to determine appropriate natural control of zika, a Flavivirus disease which spreads through bites of Aedes aegypti mosquitoes. The dynamics of the disease is modelled through a system of nonlinear ordinary differential equations, and the expression for the basic reproduction number of the disease is obtained. Sensitivity analysis is conducted on the basic reproduction number, which reveals that, biting rate of the mosquito, extrinsic incubation rate of zika virus and probability of transmission of zika virus from mosquito to human are the major parameters that increase the spread of the disease. Hence, reducing the values of these parameters will reduce the spread of zika virus disease. This suggests the use of wolbachia-infected Aedes aegypti mosquitoes to replace the natural mosquitoes since they possess the characteristics revealed by the sensitivity analysis. Stability analysis and numerical plots confirm that zika virus disease can be controlled if the natural Aedis aegypti mosquitoes are replaced by the wlbachia-infected ones.

CONTROL OF SOME NONLINEAR FUZZY SYSTEMS WITH FUZZY CONTROL INPUTS

2024-10-15T13:41:57+01:00

The study of control theory has become very popular with mathematicians, engineers and computer scientists because of its wide applications in communications and the design of artificially intelligent machines. More often than not, researchers focus on building models whose control parameters are crisp when the real life situations they are modelling are fuzzy. In the recent times, some have built models which have fuzziness into the control input. The limitation of this is that, while control may be fuzzy, uncertainty and the fuzziness in the system is not captured. This research focuses on modelling a system whose information matrix and the control input(s) are both fuzzy. The model developed was applied to a real life Chua electrical system and the numerical simulation confirms that the model is more efficient.

ON LOOPS OF VESANEN TYPE OF SMALL ORDERS

2024-06-04T16:44:37+01:00

Bruck in $1946$ showed that if $Q$ is a nilpotent loop
with $CL(Q)\leq 2$, then $Inn(Q)$ is abelian. However, Vesanen example in
\cite{mon50} showed a nilpotent loop $Q$ of order $18$ with $CL(Q)= 3$
such that the $Inn(Q)$ is not even nilpotent. These type of loops are
called, in this paper, loops of Vesanen type. Examples and properties of these type of
loops are shown and examined. The results generally showed that a loop of Vesanen type is centrally nilpotent
and can either be abelian or non-abelian but with non-nilpotent inner
mapping group. The characterization of these loops are obtained and presented.

INERTIAL ITERATION SCHEMES FOR NONEXPANSIVE MAPS AND INCLUSION PROBLEMS INVOLVING ACCRETIVE OPERATORS IN BANACH SPACES

2024-12-06T16:37:08+01:00

We study some general inertial Mann-type iteration schemes and prove that each of the scheme is an approximate fixed point sequence for nonexpansive maps in arbitrary real Banach spaces. Weak and strong convergence results are then established for fixed points of nonexpansive maps and solutions of certain important accretive-type operator inclusion problems in certain real Banach spaces. Our results extend several related recent results for the inertial generalized forward-backward splitting method.\

AN INTEREST RATE DERIVATIVE AND ITS SENSITIVITIES IN A SUBORDINATED LÉVY MARKET

2025-03-15T16:42:59+01:00

Certain financial instruments such as interest rate derivatives experience jumps due to many factors. 
Literature has shown that little has been done in considering occurrence of jumps in the interest rate market 
and its sensitivity analysis. In order to avoid risk, an investor needs to understand the effects of changes
 in the parameters of the interest rate derivatives to its output in a market with jumps; L\'{e}vy processes 
have the ability to take care of such jumps. This work was designed to derive expression for interest rate
 model driven by a subordinated L\'{e}vy process called a variance gamma process and the use of Malliavin
 calculus to compute its greeks in order to determine its sensitivities to certain changes in its parameters.