A new family of iterative methods based on an exponential model for solving nonlinear equations (Q1789994)

Summary: We present two new families of iterative methods for obtaining simple roots of nonlinear equations. The first family is developed by fitting the model \(m(x) = e^{px}(Ax^2 + Bx + C)\) to the function \(f(x)\) and its derivative \(f^{'}\), \(f^{''}\) at a point \(x_n\). In order to remove the second derivative of the first methods, we construct the second family of iterative methods by approximating the equation \(f(x)=0\) around the point \((x_n,f(x_n))\) by the quadratic equation. Analysis of convergence shows that the new methods have third-order or higher convergence. Numerical experiments show that new iterative methods are effective and comparable to those of the well-known existing methods.