TY - JOUR
T1 - Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and Dawson integral with complex arguments
AU - Zaghloul, Mofreh R.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/10
Y1 - 2024/10
N2 - We present efficient algorithms for multi-precision and multi-accuracy calculation of error functions and the Dawson integral, all with complex arguments. These algorithms achieve exceptional accuracies, ranging from 26 significant digits (SD) up to 30 SD depending on the function. In addition to the Faddeyeva or Faddeeva function, (Figure presented.) or the scaled complementary error function, (Figure presented.), the list of functions considered include the error function, erfz; the complementary error function, erfcz; the imaginary error function, erfi(z); and the Dawson integral Daw(z). These algorithms are integrated into a modern Fortran module confirming the claimed accuracies and superior efficiency compared to other competitive codes in the literature. Additionally, we highlight an observation regarding the built-in “Erfc_Scaled(x)” function included in a widely used Fortran compiler, which exhibits a significant decline in accuracy when employed in quadruple-precision arithmetic.
AB - We present efficient algorithms for multi-precision and multi-accuracy calculation of error functions and the Dawson integral, all with complex arguments. These algorithms achieve exceptional accuracies, ranging from 26 significant digits (SD) up to 30 SD depending on the function. In addition to the Faddeyeva or Faddeeva function, (Figure presented.) or the scaled complementary error function, (Figure presented.), the list of functions considered include the error function, erfz; the complementary error function, erfcz; the imaginary error function, erfi(z); and the Dawson integral Daw(z). These algorithms are integrated into a modern Fortran module confirming the claimed accuracies and superior efficiency compared to other competitive codes in the literature. Additionally, we highlight an observation regarding the built-in “Erfc_Scaled(x)” function included in a widely used Fortran compiler, which exhibits a significant decline in accuracy when employed in quadruple-precision arithmetic.
KW - Dawson integral
KW - Error functions
KW - Fortran
KW - Multiple-precision
KW - Special functions
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U2 - 10.1007/s11075-023-01727-2
DO - 10.1007/s11075-023-01727-2
M3 - Article
AN - SCOPUS:85185264770
SN - 1017-1398
VL - 97
SP - 869
EP - 887
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 2
ER -