Solution of Transcendental Equation Using Clamped Cubic Spline

Abstract

Bisection and regular false-position methods are widely used to find roots of a transcendental function f(x) in a certain interval [a,b] satisfying f(a). f(b) < 0. The paper develops a new algorithm to find roots of transcendental functions based on false position method. We use two end points of the interval to interpolate f(x) by an equivalent cubic polynomial using clamped cubic spline formula. We consider one of the roots of the interpolated function to define a new interval and to approximate the root of f(x)