Effect of truncating the Taylor series terms on derivative results of the complex conjugate approach and its applications in geophysics and statistics.

The formula for the Truncation Error (Et) was constructed from the Taylor series terms of the complex conjugate argument function that were discarded when formulating the derivative equation. The test results using 3 Test Functions show that the truncation of the series in the h²-term, the h⁴-term and the h⁶-term has insignificant effect on the computational results of the derivatives. The graphs of the computational results of the Complex Conjugate Approach derivatives with and without including Ets appear to overlap. The Ets for truncation in the h²-term, the h⁴-term and the h⁶-term are unchanged or stable for each Test Function. For Test Functions I and II, the Ets are on the order of 10⁻⁴³ and 10⁻³⁰, and for Test Function III it is on the order of 10⁻⁴⁴. This means that the Ets are extremely small, tend to zero or Et→0 so that it can be ignored. While the Relative Error (Er) of the approach for the 3 Test Functions, both those truncated in the h²-term, the h⁴-term and the h⁶-term, are on the order of 10⁻¹⁶ for Test Functions I and II, and on the order of 10⁻¹⁷ for Test Function III. The approach is very accurate because the Ers are highly small or Er→0. For its application in geophysics, the approach was used to estimate the derivative of the total magnetic field anomaly caused by a 2D finite prism-shaped source under the earth's surface, and its result was in the range of -2.3182 x 10⁷ to 1.7945 x 10⁷ nT/km. While in statistics, it was known that the population growth rates of Konawe Regency and North Konawe Regency from 2010 to 2020 were 4,585.7 and 1,696.4 persons/year, respectively. [ABSTRACT FROM AUTHOR]

Copyright of AIP Conference Proceedings is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)