Elementary Error Analysis

Abstract

In this section we will perform an error analysis of the proposed numerical integration (PART) method and explain why the log-L₂ radial transformation

$$ R(\rho ) = \log \sqrt {{\rho ^2} + {d^2}} $$

(5.64)

corresponding to ß = 2 in

$$ \rho d\rho = {\text{ }}r{'^{\beta }}{\text{ }}dR $$

(5.46)

leads to accurate numerical integration results with relatively few integration points for integrals of the type ∫_s 1/r^α dS, whilst the radial transformations corresponding to ß≠ 2 (cf. Table 5.1) give poor results. (cf. Chapter 10)