Evaluation of the numerical algorithms of the plasma dispersion function

Abstract Plasma dispersion function is an important parameter in the ionospheric physics, fast and accurate computation of this function is extremely valuable in practical use. Many numerical algorithms have been proposed, and it is very necessary to evaluate their performances. In present paper, we first introduce an alternative method to derive the plasma dispersion function and its first derivative using the differential and integral calculus method, and then compare the accuracy and efficiency of three well-known numerical algorithms (Algorithm of Steven G. Johnson, Algorithm 916, and Algorithm of Abrarov and Quine) in Matlab environment under the uniform and non-uniform distribution of the grid-points, and finally analyze the variations of the real and imaginary part of the plasma dispersion function and its first derivative preliminarily. The results show that Abrarov and Quine's algorithm performs better than other two numerical algorithms from the comprehensive viewpoint of accuracy and efficiency.