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Aug 15, 2023Open Access
This article considered the development of a twopoint hybrid method for the numerical solution of initial value problems of second order ordinary differential Equations (ODEs) using power series and exponentiallyfitted basis function. Interpolation and collocation techniques were used to derive the method. The method was implemented in predictorcorrector mode. In order to increase the accuracy of the results of the method, the predictor was designed to have same order of accuracy as the corre...
Jun 14, 2023Open Access
In this study, we have determined Green’s functions for Helmholtz integral equations in a spherical polar coordinate system in the whole plane domain with the aid of spectral Fourier transform technique. Our intended Green’s function solution has a dominant role to represent wave propagation with a high quantum wave number. The Diracdelta function also plays an important role here to represent the scattering region for wave propagation. The evaluation of the improper double integrals in the comp...
Jan 16, 2023Open Access
There is no gainsaying that the field of differential equations opened up in numerable fields of research which hitherto remains yet to be fully explored in spite of the remarkable achievements made over the centuries. In this study, the subject is given renewed interest with a view to addressing a question that is considered germane to the field of differential equations (DEs). Over the centuries, the field of ordinary differential equations (ODEs) has received varied interest from mathematicia...
Oct 25, 2022Open Access
Diabetes is a chronic disease in which the body is unable to convert the excess sugar into a useable form. It is chronic disease that is fast becoming a menace in the Kenyan communities. In this study, the response of the complicated diabetic cases is examined under a constrained hospitalisation setting. The mathematical model is formulated by incorporating the carrying capacity and the per capita hospitalization rate. The models are numerically solved in MATLAB using the explicit RungeKutta (4...
Aug 23, 2021Open Access
We introduce some new oscillation criteria for a thirdorder linear differential equation with variable coefficients in this study. We found out the corollary as a result of the Storm comparison theory and used it to prove some theorems. Through it, we were able to achieve the necessary conditions for oscillation. We concluded that the solution to the differential equation is oscillating if it is bounded from below, and also if the discriminant of the equation is negative, its solution is osci...
Feb 24, 2021Open Access
In this paper, we investigate the question of existence of nonnegative solution for some fractional boundary value problem involving pLaplacian operator, The results presented in this thesis are based on fixed point theorem, more precisely, Krasnosilski fixed point theorem, on the cones to prove the existence of a fixed point for a mathematics operator and that fixed point is a solution to the given fractional equation by combining some properties of the associated Green function. We will study...
Oct 15, 2020Open Access
In this paper, the fractional order model was adopted to describe the dynamics of measles and to establish how the virus that causes measles is transmitted as well as how to mitigate the conditions that cause the spread. We showed the existence of the equilibrium states. The threshold parameter of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the disease free and the endemic equilibrium point...
May 07, 2020Open Access
The purpose of this paper is to study the stability of nonlinear fractional Duffing equation where , by analysing the eigenvalues generated from the system of the given differential equation. Graphical results furthermore show the effect of the damping and nonlinear parameter on the system. Our contribution relies on its application to the choice of hard/soft spring in the mechanism of shock absorbers.
Apr 29, 2020Open Access
In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian decomposition formula. The solution of the differential equations has been transformed into iterative formulas that find the solution directly without the need to convert it into a nonlinear system of equations and solving it by other numerical methods that require considerable time and effort. The obtained re...
Mar 19, 2020Open Access
The second derivative method which is Astable is derived using Interpolation Collocation approach. The continuous method obtained are used to generate the main method and complementary methods to solve initial value problems of ordinary differential equation via boundary value technique. Numerical result obtained via the methods shows that the new method can compete with the existing ones in the literature.
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