Erratum to “Approximate analytical solutions for primary chatter in the non-linear metal cutting model”

2004 ◽  
Vol 272 (1-2) ◽  
pp. 469-470
Author(s):  
J. Warmiński ◽  
G. Litak ◽  
M.P. Cartmell ◽  
R. Khanin ◽  
M. Wiercigroch
Keyword(s):  
Analytical Solutions ◽  
Metal Cutting ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Cutting Model

scholarly journals APPROXIMATE ANALYTICAL SOLUTIONS FOR PRIMARY CHATTER IN THE NON-LINEAR METAL CUTTING MODEL

2003 ◽  
Vol 259 (4) ◽  
pp. 917-933 ◽  
Author(s):  
J. WARMIŃSKI ◽  
G. LITAK ◽  
M.P. CARTMELL ◽  
R. KHANIN ◽  
M. WIERCIGROCH
Keyword(s):  
Analytical Solutions ◽  
Metal Cutting ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Cutting Model

An Approximate Method for Non -Darcy Radial Gas Flow

1964 ◽  
Vol 4 (02) ◽  
pp. 96-114 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Linear Equation ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Gas Flow ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Non Linear Equation ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Flow Law

Abstract Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is shown to be very good. Some observations on the interpretation of gas well tests are made. Introduction The flow of gases in porous media is a problem that has been the subject of much study in recent years, and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law (1) leads to a non-linear equation of the form (2) in a homogeneous medium, assuming an equation of state(3) It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form (4) This form of equation was first suggested by Forchheimer and, later, Katz and Cornell, and Irmay, developed a similar equation. Houpeurt derived this form of equation using the concept of an idealized pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type, for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al., and Aronofsky and Jenkins, but the latter solutions, apart from the simple linearization of equation [2] to yield a diffusion equation in p2, are not so well-known. SPEJ P. 96ˆ

A Note on the Application of Operational Methods to Certain Non-Linear Problems

1976 ◽  
Vol 13 (3) ◽  
pp. 219-224 ◽  
Author(s):  
J. O. Flower
Keyword(s):  
Laplace Transform ◽  
Analytical Solutions ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Linear Problems ◽  
Operational Methods

In recent years some effort has been devoted to obtaining approximate analytical solutions to a certain class of non-linear problems using multi-dimensional Laplace transform theory. This note demonstrates that ordinary Laplace transform theory is very often adequate for this task and is, indeed, superior for many problems in this area.

scholarly journals Approximate analytical solutions of non-linear local fractional heat equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 837-841 ◽  
Author(s):  
Shuxian Deng
Keyword(s):  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Non Linear

Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

scholarly journals Application of DGJ method for solving non-linear local fractional heat equations

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1571-1576 ◽  
Author(s):  
Shu-Xian Deng ◽  
Xin-Xin Ge
Keyword(s):  
Heat Equation ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Heat Equations ◽  
Initial Value ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Non Linear

In this paper, the initial value problem for a new non-linear local fractional heat equation is considered. The fractional complex transform method and the DGJ decomposition method are used to solve the problem, and the approximate analytical solutions are also obtained.

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