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.
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