Finding roots of nonlinear functions has always been one of the most basic and important subjects of numerical analysis. The problem arise in diverse areas such as chemistry, engineering, finance and biology. A root occurs when a function f(x) intersects the x-axis, i.e., where f(x)=0. There are numerous methods for finding roots.
The Brown-Johnson Method was developed by combining aspects of the following methods: bisection Method, Newton’s Method, and secant Method. Secant and tangent lines are used to restrict the range that the root could lie within, and then the bisection Method is used to approximate the root. The Brown-Johnson method converges at almost the same rate as Newton’s method, and also guarantees convergence when given an appropriate initial interval.
Figure 7: Root-finding method
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