The Generalized Fourier Series Method by Christian Constanda & Dale Doty

Author:Christian Constanda & Dale Doty
Language: eng
Format: epub
ISBN: 9783030558499
Publisher: Springer International Publishing

In addition to producing ψ (78), the representation formula (6.22) also yielded the approximation

When the rigid displacement f is computed with 200 points x (k), the error for f (78) can be approximated by

6.3.4 Error Analysis

The approximation ψ (n), n = 3N + 3, is computed with N equally spaced points x (k) on ∂S ∗, and the additional point . The relative error

as a function of N determines the efficiency and accuracy of the computational procedure. However, since the exact expression of Tu is not known in this example, an accurate error analysis cannot be performed.

As a substitute, we propose instead an indirect route to obtaining a measure of partial validation of our calculations. We use the approximation ψ (78) of Tu on ∂S as the boundary condition for an exterior Neumann problem and compute the approximate boundary value of the solution to the latter by means of the scheme designed in Chap. 7. If our method is sound, then augmented with f (78) given by (6.37) should be close to (see Sect. 6.3.1). Figure 6.16 shows the components of .

Fig. 6.16Components of in polar coordinates

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