Asian Research Journal of Mathematics
EISSN : 2456-477X
Published by: Sciencedomain International (10.9734)
Total articles ≅ 474
Latest articles in this journal
Asian Research Journal of Mathematics pp 48-56; https://doi.org/10.9734/arjom/2021/v17i930330
There are studies on parametric solutions of system of Linear Diophantine equations based on uni-modular reductions of the coefficient matrix. In this paper we generate parametric solutions, with uni-modular row reductions on the coefficient matrix, based on the steps used in obtaining gcd of the coefficients in a row by crushing method. This application of gcd by crushing specifies an order for the row reductions and enables to give algorithm for the computations.
Asian Research Journal of Mathematics pp 34-47; https://doi.org/10.9734/arjom/2021/v17i930329
The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to treat some highly stiff linear problems. The new approach compute clearly showed that the method is reliable, efficient and gives faster convergence when compared with those in literature.
Asian Research Journal of Mathematics pp 20-33; https://doi.org/10.9734/arjom/2021/v17i930328
MHD flow has a wide range of industrial applications such as MHD propulsion for space exploration, cooling of nuclear reactors, electronic packages, microelectronic devices, and many more. Due to this, a study on the MHD boundary layer flow of a viscous incompressible fluid over an exponentially stretching sheet with an inclined magnetic field in presence of thermal radiation is analyzed. The continuity, momentum, and energy equations governing the fluid motion are obtained. They are then transformed into a system of nonlinear ordinary differential equations using suitable similarity transformation variables. The resulting nonlinear ordinary differential equations are then transformed to a system of first-order ordinary differential equations and the numerical solution is executed using the collocation method. The effects of the magnetic field, angle of inclination, radiation, Prandtl number, and the exponential stretching of the sheet on the velocity and temperature of the fluid are discussed. It is observed that velocity increases as the sheet is stretched and decreases as the magnetic field and angle of inclination of the magnetic field increases. Temperature increases as magnetic field, angle of inclination, and radiation increase and lowers as the stretching and stratification parameter of the sheet and Prandtl number increases. The findings of this study are in agreement with other previously related work done.
Asian Research Journal of Mathematics pp 11-19; https://doi.org/10.9734/arjom/2021/v17i930327
In this article, the Laplace decomposition method and Modified Laplace decomposition method have been employed to obtain the exact and approximate solutions of the Klein-Gordon equation with the initial profile. An approximate solution obtained by these methods is in good agreement with the exact solution and shows that these approaches can solve linear and nonlinear problems very effectively and are capable to reduce the size of computational work.
Asian Research Journal of Mathematics pp 1-10; https://doi.org/10.9734/arjom/2021/v17i930326
The investigation of dissipative heat and species diffusion of a conducting liquid under the combined influence of buoyancy forces in a moving plate is examined in the existence of magnetic field. The flowing liquid heat conductivity and viscosity are taken to be linearly varied as a temperature function. The governing derivative equations of the problem are changed to anon-linear coupled ordinary derivative equations by applying similarity quantities. The dimensionless model is solved using shooting technique along with the Runge-Kutta method. The outcomes for the flow wall friction, heat gradient and species wall gradient are offered in table and qualitatively explained. The study revealed that the Newtonian fluid viscosity can be enhanced by increasing the fluid flow medium porosity and the magnetic field strength. Hence, the study will improve the industrial usage of Newtonian working fluid.
Asian Research Journal of Mathematics pp 76-86; https://doi.org/10.9734/arjom/2021/v17i830324
We present in this research work, mathematical modeling of the transmission dynamics of measles using treatment as a control measure. We determined the Disease Free Equilibrium (DFE) point of the model after which we obtained the Basic Reproduction Number ( R0 ) of the model using the next generation approach. The model Endemic Equilibrium (EE) point was also determined after which we performed Local Stability Analysis(LAS) of the Disease Free Equilibrium point and result shows that the Disease Free Equilibrium point of the model would be stable if ( R0 <1). Global Stability Analysis (GAS) result shows that, ( R0 ≤ 1) remains the necessary and sufficient condition for the infection to go into extinction from a population. We carried out Sensitivity Analysis of the model using the Basic Reproduction Number and we discovered that ( δ , μ, ν , θ ) are sensitive parameters that should be targeted towards control intervention strategy as an increase in these values can reduce the value of ( R0 ) to a value less than unity and such can reduce the spread of measles in a population. Model simulation was carried out using mat lab software to support our analytical results.
Asian Research Journal of Mathematics pp 54-75; https://doi.org/10.9734/arjom/2021/v17i830323
The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.
Asian Research Journal of Mathematics pp 44-53; https://doi.org/10.9734/arjom/2021/v17i830322
Some further theoretic properties of scheme called Γ1 non deranged permutations, the permutation which fixes the first element in the permutations were identified and studied in relation to admissible inversion in this paper. This was done first through some computation on this scheme using prime number p ≥ 5, the admissible inversion descent aid (ωp-1) is equi-distributed with descent number des (ωp-1) and also showed that the admissible inversion set Ai (ωi ) and admissible inversion set Ai (ωp-i ) are disjoint.
Asian Research Journal of Mathematics pp 30-43; https://doi.org/10.9734/arjom/2021/v17i830321
In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.
Asian Research Journal of Mathematics pp 14-29; https://doi.org/10.9734/arjom/2021/v17i830320
Existence of Positive Solution For a Fourth-order Differential System where µ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to the time and space variables. By fixed point theorem in cones, the existence is established for singular differential system. The results obtained herein generalize and improve some known results including singular and non-singular cases.