Research Article
New Theorems and Formulas to Solve Fourth Degree Polynomial Equation in General Forms by Calculating the Four Roots Nearly Simultaneously
Issue:
Volume 11, Issue 6, December 2023
Pages:
95-105
Received:
6 October 2023
Accepted:
2 November 2023
Published:
17 November 2023
Abstract: This paper presents new formulary solutions for fourth degree polynomial equations in general forms, where we present four solutions for any fourth-degree equation with real coefficients, and thereby having the possibility to calculate the four roots of any quartic equation nearly simultaneously. In this paper, the used logic to determine the solutions of a fourth-degree polynomial equation enables to deduce if the polynomial accepts complex roots with imaginary parts different from zero and how many of them there are. As a result, we are proposing six new theorems, where two among them are allowing to calculate the four roots nearly simultaneously for any fourth-degree polynomial equation in simple forms and complete forms, whereas the other four theorems are allowing to deduce the number of complex roots with imaginary parts different from zero before conducting further fetching for the values. Furthermore, the proposed formulas in this paper are building the ground to concretize precise solutions for polynomial equations with degrees higher than four while relying on radical expressions. Each proposed theorem in this paper is presented along with a detailed proof in a scaling manner starting from propositions based on precise formulas whereas building on progressive logic of calculation and deduction. Each formulary solution in proposed theorems is based on a distributed group of radical expressions designed to be neutralized when they are multiplied by each other, which allow the elimination of complexity while reducing degrees of terms. All presented theorems are developed according to a specific logic where we engineer the structure of solutions before forwarding calculations to express the precis formulas of roots.
Abstract: This paper presents new formulary solutions for fourth degree polynomial equations in general forms, where we present four solutions for any fourth-degree equation with real coefficients, and thereby having the possibility to calculate the four roots of any quartic equation nearly simultaneously. In this paper, the used logic to determine the solut...
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Research Article
A Comparative Study of Numerical Methods for Solving Initial Value Problems (IVP) of Ordinary Differential Equations (ODE)
Md. Monirul Islam Sumon*,
Md. Nurulhoque
Issue:
Volume 11, Issue 6, December 2023
Pages:
106-118
Received:
24 August 2023
Accepted:
8 October 2023
Published:
21 November 2023
Abstract: Numerical methods for solving Ordinary Differential Equations differ in accuracy, performance, and applicability. This paper presents a comparative study of numerical methods, mainly Euler’s method, the Runge-Kutta method of order 4th & 6th and the Adams-Bashforth-Moulton method for solving initial value problems in ordinary differential equations. Our aim in this paper is to show that which method gives better accuracy for the initial value problem in numerical methods. Comparisons are made among the direct method, Euler’s method, Runge-Kutta fourth and sixth order and the Adams-Bashforth-Moulton method for solving the initial value problem. The comparisons with error analysis are also shown in the graphical and tabular form. MATHEMATICA 5.2 software is used for programming code and solving the particular problems numerically. It is found that the calculated results for a particular problem using the Runge-Kutta fourth order give good agreement with the exact solution, whereas the Runge-Kutta sixth order defers slightly for a particular problem. Approximate solution using the Adams-Bashforth method with error estimation is also investigated. Moreover, we are also investigated of the Euler methods, the Runge-Kutta methods of order 4th & 6th and the Adams-Bashforth method for solving a particular initial value problem. Finally, it is found that the Adams-Bashforth method gives a better approximation result among the others mentioned methods for solving initial value problems in ordinary differential equations.
Abstract: Numerical methods for solving Ordinary Differential Equations differ in accuracy, performance, and applicability. This paper presents a comparative study of numerical methods, mainly Euler’s method, the Runge-Kutta method of order 4th & 6th and the Adams-Bashforth-Moulton method for solving initial value problems in ordinary differential equations....
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Research Article
A Mathematical Model of the Transmission of COVID-19 in Ghana
Ernest Danso-Addo,
Samuella Boadi*,
John Cobbinah
Issue:
Volume 11, Issue 6, December 2023
Pages:
119-129
Received:
21 September 2023
Accepted:
12 October 2023
Published:
8 December 2023
Abstract: The COVID-19 pandemic posed a serious threat to health and the global economy of the affected nations. Despite several measures to mitigate the transmission of the disease, there is a rise in the number of infections and death remain tremendous worldwide. This study used a deterministic model based on Susceptible-Latent-Infected-Hospitalized-Vaccinated-Recovered (SLIHVR) model to investigate the dynamics of the disease in Ghana. Data from daily reported cases of COVID-19 in Ghana between 15 March and 31 March 2021 were used to estimate the parameters of the model. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The numerical simulation of the model was done to ascertain the long-run evolution of COVID-19. The findings indicated that the disease-free equilibrium was locally asymptotically stable whenever Rn<1 and the endemic equilibrium was asymptotically stable provided Rn>1. The was useful in understanding the dynamic mechanisms of the transmission and prevention of COVID-19 infection in Ghana. The study concluded that vaccinating a larger proportion of the populace was needed to control the disease.
Abstract: The COVID-19 pandemic posed a serious threat to health and the global economy of the affected nations. Despite several measures to mitigate the transmission of the disease, there is a rise in the number of infections and death remain tremendous worldwide. This study used a deterministic model based on Susceptible-Latent-Infected-Hospitalized-Vaccin...
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