The phrase "analytical integration" is correct and usable in written English.
It can be used in contexts related to mathematics, statistics, or data analysis, where it refers to the process of finding an integral using analytical methods.
Example: "The researcher employed analytical integration to solve the complex equations presented in the study."
Alternatives: "calculus integration" or "mathematical integration".
The speed of improvement is due to the analytical integration of the integrals involved in the calculation of E [g|Y].
There are two main reasons for numerical integration: analytical integration may be impossible or infeasible, and in integrating tabulated data rather than known functions.
The hydrodynamic model of the TAPINS is formulated using the one-dimensional momentum integral model, which is based on the analytical integration of the momentum equation around the closed loop in the system.
Fourier integral is solved using a combination of numerical and analytical integration resulting in a continuous transient function in the frequency domain.
Green's functions, expressed by the line integrals over a semi-circle, have a simple structure that allows analytical integration over the boundary elements.
Solution of two-dimensional Poisson's equations is carried out by BEM based on Galerkin Vector Method in which the integrals that appear in the boundary element method are expressed by analytical integration.
THEM analysed the data and drafted the manuscript; TRS simulated the data; RS performed literature search on EM type of algorithms and came up with the ICE algorithm; JAW derived the analytical integrations and helped drafting the manuscript.
However, to date no one has attempted a meta-analytical integration of this research stream.
It is shown that a simple nonlinear lumped parameter model is sufficient to schematise the gyroscope and that a semi-analytical integration method allows to quickly determine both stable and unstable branches of the system's dynamic response.
Next, a novel semi-analytical integration scheme, called the phase space linearization method (PSL) is developed to obtain stable and unstable periodic solutions of forced as well as unforced non-linear oscillators and also the damped separatrices.
In this paper, we present a semi-analytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes.
