Evaluating of Dawson's Integral by solving its differential equation using orthogonal rational Chebyshev functions

摘要

Dawson's Integral is u(y) equivalent to exp(-y(2)) integral(y)(0) exp(z(2))dz. We show that by solving the differential equation du/dy + 2yu = 1 using the orthogonal rational Chebyshev functions of the second kind, SB2n(y; L), which generates a pentadiagonal Petrov-Galerkin matrix, one can obtain an accuracy of roughly (3/8)N digits where N is the number of terms in the spectral series. The SB series is not as efficient as previously known approximations for low to moderate accuracy. However, because the N-term approximation can be found in only O(N) operations, the new algorithm is the best arbitrary-precision strategy for computing Dawson's Integral. (C) 2008 Elsevier Inc. All rights reserved.