Back to Search
Start Over
COMPUTATION OF THE COMPLEX ERROR FUNCTION USING MODIFIED TRAPEZOIDAL RULES.
- Source :
-
SIAM Journal on Numerical Analysis . 2021, Vol. 59 Issue 5, p2346-2367. 22p. - Publication Year :
- 2021
-
Abstract
- In this paper we propose a method for computing the Faddeeva function w(z):... erfc(-iz) via truncated modified trapezoidal rule approximations to integrals on the real line. Our starting point is the method due to Matta and Reichel (Math. Comp. 25 (1971), pp. 339-344) and Hunter and Regan (Math. Comp. 26 (1972), pp. 339-541). Addressing shortcomings flagged by Weideman (SIAM. J. Numer. Anal. 31 (1994), pp. 1497-1518), we construct approximations which we prove are exponentially convergent as a function of N+1, the number of quadrature points, obtaining error bounds which show that accuracies of 2x10-15 in the computation of w(z) throughout the complex plane are achieved with N=11, this confirmed by computations. These approximations, moreover, provably achieve small relative errors throughout the upper complex half-plane where w(z) is non-zero. Numerical tests suggest that this new method is competitive, in accuracy and computation times, with existing methods for computing w(z) for complex z [ABSTRACT FROM AUTHOR]
- Subjects :
- *ERROR functions
*FADDEEVA function
*LINE integrals
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 59
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 153348222
- Full Text :
- https://doi.org/10.1137/20M1373037