Sentence examples for first order approximate from inspiring English sources

A general procedure for obtaining the first order approximate solution is presented through an application of the Bogoliubov-Mitropolsky technique.

The first order approximate reliability method (FARM) and second order approximate reliability method (SARM) are formulated based on evidence theory in this paper.

The validity of the developed analysis is highlighted by comparing the first order approximate solutions with the results of numerical integration of the original equations.

The first order approximate solutions of a set of non-liner differential equations, which is established by using Kane's method and governs the planar motion of beams under a large linear motion of basement, are systematically derived via the method of multiple scales.

A very simple generalization, using Jacobian elliptic functions, of the usual Fourier series, appropriate for non-linear systems, is used to study the first order approximate solution of the generalized van der Pol oscillators Ẍ+AX+2BX3+ϵ z3+z2X2+z1X4 dotX=0.

Temperature in the film is calculated by a first order approximate energy equation that includes heat transfer between the film and its boundaries.

This paper presents a novel approach to the design of low-thrust trajectories, based on a first order approximated analytical solution of Gauss planetary equations.

A seventh order approximate polynomial function is used to explore the effects of these parameters.

Stability diagrams of the first and the second order approximate solutions are obtained by using the multiple scale perturbation method.

The stability diagrams show that there exist significant difference between the first and the second order approximate solutions.

The accuracy of the calculated elastic strain and electric fields is improved greatly by a second order approximate solution (OAS).