An Analytical Study of Alternative Method for Solving Lotka’s Law with Simpson’s 1/3 Rule

Abstract

This paper deals with a new stochastic method to solve Lotka’s Law with higher degree of Newton-Cotes Quadrature Rule as an alternate method to existing solution of the value determination of the constant part of the power law; so far, M.L. Pao gave a solution with an equation to determine the area under the curve with numerical integration rule with degree=1 which is also known as Trapezoidal Rule. Here, next higher degree 2, popularly known as Simpson’s 1/3 rule at closed interval [x1,] has been used to establish a deterministic equation form to solve authors’ productivity realized through Lotka’s Law. Re-estimating the value of C with higher degree quadrature rule is very crucial as the probability of inclusion of more area and exclusion of unnecessary area under the curve is more precise. Another area of investigation is the determination of p value (Pao determined p=20), i.e. whether p=20 can be altered? Or equation derived through Simpson’s 1/3 rule, whether it can give a minimal residual error beyond p=20. This paper is dedicated to build up a mathematical equation to solve the constant value(C) of the Lotka’s law equation as well as enlighten all these investigating points.