11 Numerical Evaluation of Integrals in Laplace Domain Anisotropic …
163
Fig. 11.3 Amplitude function f 1
i j (ψ)
Fig. 11.4 Amplitude function f 2
i j (ψ)
In Fig. 11.6, phase functions q m (ψ), m = 1, 3, are shown. We make a special note
that q 1 (ψ) and q 3 (ψ) have stationary points. The positions of stationary points are
clearly seen as zeros of derivatives of phase functions q
m (ψ) as depicted in Fig. 11.7.
In Figs. 11.8 and 11.9, errors err(I 1 ) and err(I 2 ) are depicted versus total number
of integrand evaluations for fixed value ω = 500 for the following orders of EvansWebster method (EW) uniformly applied on subintervals of integration: 5, 6, 7
163
Fig. 11.3 Amplitude function f 1
i j (ψ)
Fig. 11.4 Amplitude function f 2
i j (ψ)
In Fig. 11.6, phase functions q m (ψ), m = 1, 3, are shown. We make a special note
that q 1 (ψ) and q 3 (ψ) have stationary points. The positions of stationary points are
clearly seen as zeros of derivatives of phase functions q
m (ψ) as depicted in Fig. 11.7.
In Figs. 11.8 and 11.9, errors err(I 1 ) and err(I 2 ) are depicted versus total number
of integrand evaluations for fixed value ω = 500 for the following orders of EvansWebster method (EW) uniformly applied on subintervals of integration: 5, 6, 7