Bidimensional Fluid-Film Flows of Stokesian Fluids

1982 ◽  
Vol 104 (2) ◽  
pp. 227-233
Author(s):  
Patrick Bourgin ◽  
Bernard Gay
Keyword(s):  
Laminar Flow ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Differential System ◽  
Analytic Method ◽  
Shearing Stress ◽  
Flow Equations ◽  
Approximate Analytic Method ◽  
Film Flows

The bidimensional flow equations of a Stokesian fluid are solved for the case of steady, incompressible, and laminar flow between two arbitrary moving surfaces separated by a small gap. The stress T22 and the shearing stress at one of the walls are coupled through nonlinear integro-differential equations, depending on the viscous function only. The form of this differential system is specified for the equations derived from the theory of phenomenological macrorheology, as developed by Reiner and Rivlin. The solution is proved to be unique under certain conditions and for adequate boundary conditions. An example is worked out in the particular case of one single non-Newtonian parameter. The problem is solved in two different ways, using an approximate analytic method and a numerical method. The conception of the latter allows to generalize it by introducing only slight modifications into the program.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

The Behaviour of a Clamped Circular Plate in Compression

1961 ◽  
Vol 12 (1) ◽  
pp. 51-64 ◽  
Author(s):  
A. N. Sherbourne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Circular Plate ◽  
Digital Computer ◽  
Large Deflection ◽  
Theoretical Solution ◽  
Uniform Compression ◽  
Simply Supported ◽  
Von Karman

SummaryA theoretical solution is presented for the problem of the clamped circular plate loaded in uniform compression. The solution employs a numerical method programmed for a digital computer. Instead of solving the classical von Kármán large deflection equations, a step-by-step integration of the elastic differential equations of equilibrium is carried out until suitable boundary conditions are attained. The method is an extension of one developed earlier to explain the behaviour of the simply-supported plate.

FORCES, MOMENTS, ROTATIONS, AND DISPLACEMENTS OF POLYNOMIAL-SHAPED CURVED BEAMS

2010 ◽  
Vol 10 (01) ◽  
pp. 77-89 ◽  
Author(s):  
LAZARO GIMENA ◽  
PEDRO GONZAGA ◽  
FAUSTINO GIMENA
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
The Other ◽  
Curved Beams ◽  
Fourth Degree ◽  
Linear Ordinary Differential Equations ◽  
Parabolic Shape

This paper deals with curved beams with polynomial free geometry. The problem is approached analytically and the differential equations that govern the mechanical behavior of curved beams are presented. A system of twelve linear ordinary differential equations is solved using either an analytical or a customized numerical method with boundary conditions. Results of the different components of forces, moments, rotations, and displacements are given and plotted in the examples for different polynomial-shaped beams of the fourth degree. It is concluded from the present analyses that the parabolic shape has better response to distributed loads than the other polynomial-shaped beams considered.

On the spread of fire in a homogeneous steppe massif along an inclined underlying surface

2012 ◽  
Vol 9 (1) ◽  
pp. 26-31
Author(s):  
N.A. Asylbaev ◽  
I.K. Gimaltdinov
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Numerical Method ◽  
Underlying Surface ◽  
Two Dimensional ◽  
System Of Differential Equations ◽  
Discrete Form ◽  
Surface System ◽  
Volume Method

The formulation and results of the numerical solution of the problem of the spread of steppe fire in two-dimensional case on an inclined underlying surface. System of differential equations in partial derivatives with the corresponding initial and boundary conditions is reduced to a discrete form using the check volume method. Grid equations arising in the process of discretization, are solved using a numerical method.

A parameter uniform essentially first-order convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction–diffusion type with initial and Robin boundary conditions

2019 ◽  
Vol 12 (01) ◽  
pp. 1950001 ◽  
Author(s):  
R. Ishwariya ◽  
J. J. H. Miller ◽  
S. Valarmathi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Diffusion Type ◽  
Parabolic Boundary ◽  
First Order ◽  
Robin Boundary

In this paper, a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction–diffusion type with initial and Robin boundary conditions is considered. The components of the solution [Formula: see text] of this system are smooth, whereas the components of [Formula: see text] exhibit parabolic boundary layers. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Spectral Methods

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Algebra ◽  
Spectral Methods ◽  
Differential Operators ◽  
Higher Dimensions ◽  
Standard Linear ◽  
Sommerfeld Equation ◽  
Spectral Discretization

Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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