Remarks on the Limitations of the Third Romberg Integration Method in Numerical Extrapolation

Grace O. Akinlabi and George S. Nduka
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Grace O. Akinlabi: Department of Mathematics, Covenant University, Ota, Nigeria
George S. Nduka: Department of Mathematics, Dennis Osadebay University, Asaba, Nigeria

International Journal of Research and Scientific Innovation, 2024, vol. 11, issue 11, 664-669

Abstract: The Romberg extrapolation method (REM) is a powerful numerical integration tool that uses successive applications of the trapezoidal rule and Richardson extrapolation to obtain highly precise estimates of definite integrals. While the third Romberg extrapolates, in particular, produces a refined output by canceling higher-order error words, it has inherent restrictions in its use. This work investigates these limits, which include assumptions about function smoothness, computational complexity, and inefficiencies in dealing with discontinuities or highly oscillatory functions. Two worked examples are offered to exemplify the behaviour and performance of the third Romberg extrapolate in real applications, illustrating both its strengths and weaknesses.

Date: 2024
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