ABSTRACT
Standard root-finding techniques are commonly applied to boundary value problems and property estimation. They are usually chosen so that the iteration never gets outside the best bracketing bounds obtained at any stage in the calculation. An algorithm developed in the 1960s by van Wijngaarden, Dekker and others has superlinear convergence and stays within the bracketed root. An improved algorithm presented by R. P. Brent guarantees convergence if there is a root inside the bracketed interval. A hybrid root-finding method is developed that efficiently finds an accurate root. This method is an application of a high-order Newton’s and the bisection methods. The hybrid root finder is a useful tool for finding the roots of transcedental equations one encounters when solving the diffusion equation.
