Quadratically convergent algorithm for computing real root of non-linear transcendental equations

The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton-Raphson method is, it fails when first derivative is zero or approximately zero.

The proposed method implemented the failure condition of Newton-Raphson method with better convergence. Error calculation has been discussed for certain real life examples using Bisection, Regula-Falsi, Newton-Raphson method and new proposed method. The computed results show that the new proposed quadratically convergent method provides better convergence than other methods.