Laplace’s method – Knowledge and References

Laplace's method

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The Asymptotic Approximation of Integrals

Published in Alan W. Bush, Perturbation Methods for Engineers and Scientists, 2018

An attempt at a straightforward application of Laplace’s method yields an incorrect result. We have () Γ(p+1)=∫0∞eplnte−tdt,

Tools For Analysis

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Purchase Book

Published in James J Y Hsu, Nanocomputing, 2017

James J Y Hsu

by assuming the peak occurs at the origin. There are limitations and variations to this theorem, if the maximum happens to be at the inte-gration boundary or other peaks are equally important, for example. The general concept however, is well described by Eq. (2.26). The Laplace method could be the basis for other approximate methods such as the Saddle Point Method.

An analytic approach for resource efficient parametric simulation of electronic circuits

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Journal Information

Published in EPE Journal, 2020

Mario Schenk, Annette Muetze, Klaus Krischan

The module ‘Solve ODEs’ generally solves the ODE system from the SubCircuit-Model (6). The proposed approach uses the built-in ODE solver from Maple. Out of the different solver methods and options available, the proposed approach uses the Laplace method. When the ODE system from the SubCircuit-Model has been solved once, the solution is stored and, therefore, a further solving of the ODE system is no longer necessary for this state . The analytic solution of the ODE System (12) from the interconnected SubCircuit-Model in Section 2.2 is shown in symbolic form (17).