11 Numerical Evaluation of Integrals in Laplace Domain Anisotropic …
167
Fig. 11.11 err(I 2 ) for 1 ≤ ω ≤ 1000, N = 8, 9, 10, and 300 integrand evaluations
Fig. 11.12 err(I 2 ) for 1 ≤ ω ≤ 1000 and different number of subintervals of integration
number of integrand evaluations required for err(I 2 ) ≤ 1 × 10
−10 is depicted versus
frequency 1 ≤ ω ≤ 1000 for GL and our procedure with EW method orders N = 5,
6, 7, 8, 9, and 10. As expected, GL performs better for lower frequencies ω ≤ 100.
Again, as ω increases, the required number of integrand evaluations decreases for
our procedure.
We introduce a dimensionless performance coefficient
η =
number of integrand evaluations for GL
number of integrand evaluations for EW − based procedure
167
Fig. 11.11 err(I 2 ) for 1 ≤ ω ≤ 1000, N = 8, 9, 10, and 300 integrand evaluations
Fig. 11.12 err(I 2 ) for 1 ≤ ω ≤ 1000 and different number of subintervals of integration
number of integrand evaluations required for err(I 2 ) ≤ 1 × 10
−10 is depicted versus
frequency 1 ≤ ω ≤ 1000 for GL and our procedure with EW method orders N = 5,
6, 7, 8, 9, and 10. As expected, GL performs better for lower frequencies ω ≤ 100.
Again, as ω increases, the required number of integrand evaluations decreases for
our procedure.
We introduce a dimensionless performance coefficient
η =
number of integrand evaluations for GL
number of integrand evaluations for EW − based procedure