Second-order complex Newton root-finding algorithm for determining resonant modes of a nontrivial laser system
Copyright policy )Second-order complex Newton root-finding algorithm for determining resonant modes of a nontrivial laser system
The paper deals with a second-order algorithm obtained by a three-terms Taylor series expansion. There is a misprint in the main equation (10). The correct expression of (10) is given by \[ x_{i+1}= x_ i- {f'(x_ i)\over f''(x_ i)}\pm\sqrt{{[f'(x_ i)]^ 2- 2f(x_ i)f''(x_ i)\over f''(x_ i)^ 2}}.\tag{10} \] The authors don't indicate how the sign \(+\) or \(-\) is taken in (10) in order to obtain a convergent method. An error estimation and some examples are given.
- University of Dayton United States
numerical examples, complex Newton root-finding algorithm, iterative root-finding algorithm, Lasers, masers, optical bistability, nonlinear optics, second-order algorithm, Taylor series expansion, Computer Science Applications, General theory of numerical methods in complex analysis (potential theory, etc.), error estimation, Modelling and Simulation, Numerical computation of solutions to single equations, resonant modes of a nontrivial laser system
numerical examples, complex Newton root-finding algorithm, iterative root-finding algorithm, Lasers, masers, optical bistability, nonlinear optics, second-order algorithm, Taylor series expansion, Computer Science Applications, General theory of numerical methods in complex analysis (potential theory, etc.), error estimation, Modelling and Simulation, Numerical computation of solutions to single equations, resonant modes of a nontrivial laser system
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