This paper focuses on the construction and implementation of an improved secant method for finding the root of a polynomial. The arithmetic mean in the Marouane’s method was replaced by the geometric mean. The result shows that the method converges compete favorably with other methods in literature and efficient as the two points in the conventional secant methods has been reduced to only one fixed point.
The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.
Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.
In this work, a numerical analysis of a mathematical model for the preservation of forestry biomass is investigated. The model is divided into three compartments as density of forest biomass, density of wood based industries and density of synthetic industries. The Laplace Decomposition Method is used to obtain approximate solutions in the form of infinite series. Numerical justification is performed on the model parameter values with the aid of Maple 18 software to obtain the results. The behavior of the results obtained, is presented graphically. From the results, it was observed that the population of forest biomass increases exponentially as we increase the competitive effect of forest biomass c 1 , on wood industries. It was also observed that the wood based industries will have no depleting effect on the forest biomass even when the competitive effect parameter of wood based industries c 2 , on forest biomass was increased, and this was likened to increase awareness on synthetics as alternatives to wood, government control policies on deforestation, and an increase in prices of timber. It was also obvious from the result that as sufficient synthetic materials are supplied to the synthetic industries, the industries explode exponentially with time, and would serve as a good alternative to wood inpreserving the forestry biomass.
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