Cubic Bezier Homotopy Function for Solving Exponential Equations

Abstract

In this study, the new Cubic Bezier homotopy function has been extended from Quadratic Bezier homotopy function for implementation with single exponential equations. The extended function is a combination of the Bezier curve and homotopy function that was based on De Casteljau algorithm. The function will include the target function and the auxiliary function. The target function is the exponential equation while the auxiliary function selected must be controllable and easy to be solved. Then, the extended function has solved by using Newton Homotopy Continuation Method to compute the approximate solutions, accuracy of the approximate solutions and maximum absolute error of the solutions. The analysed results proved that these Cubic Bezier Homotopy function show better approximate solutions, accuracy of the approximate solutions and maximum absolute error of the solutions compared to Quadratic Bezier homotopy function.