Modification of False-Position Method to Improve Its Convergence

Root finding of polynomials is necessary for many engineering applications. Analytical root-finding methods may not be applicable when the orders of the polynomials are high or the objective function has fractional orders. In the literature many complex numerical root finding algorithms exist but they are not suitable for undergraduate courses. In this study a drawback of the False-Position method which occurs when the magnitudes of the function values at boundary points are disproportionate is eliminated. The highest function value at the boundary point is divided by the number of iteration in which the corresponding side is unchanged. This small modification improved the convergence capability of the False-Position method without compromising its simplicity. The modified algorithm is tested on two case study problems and the modified False-Position algorithm provided better results than its original state. In addition to this, the algorithm provided better results than bisection and secant root-finding algorithms. However, the convergence rate of Newton-Raphson is still better than the modified False-Position algorithm. The modified False-Position algorithm can be implemented for engineering problems and undergraduate courses due to its simplicity and relatively fast convergence capability.