scholarly journals Criticality dependence on data and parameters for a problem in combustion theory

1986 ◽  
Vol 27 (4) ◽  
pp. 416-441 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Boundary Data ◽  
Main Part ◽  
Original Problem ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Central Problem ◽  
Good Agreement

AbstractA central problem in the theory of combustion, consisting of a nonlinear parbolic equation together with initial and boundary conditions, is considered. The influence of the initial and boundary data examined. In the main part of the study, a two-step linearization is developed such that the interesting features of the original problem are given by the solution of a non-liner and ordinary differential equation. Approximate solutions are obtained and upper and lower solutions are used to assess the validity of the approximations. Whenever possible, results are compared with those obtained previously and there is good agreement in all cases.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals Harmonic Balance Solution Of Coupled Nonlinear Non-Conservative Differential Equation

2013 ◽  
Vol 32 ◽  
pp. 1-14
Author(s):  
M Saifur Rahman ◽  
M Majedur Rahman ◽  
M Sajedur Rahaman ◽  
M Shamsul Alam
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Limit Cycle ◽  
Nonlinear Differential Equation ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Balance Method ◽  
Balance Solution ◽  
Good Agreement

A modified harmonic balance method is employed to determine the second approximate solutions to a coupled nonlinear differential equation near the limit cycle. The solution shows a good agreement with the numerical solution. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13640 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 1 – 14

scholarly journals On a nonlinear boundary value problem involving a small parameter

1962 ◽  
Vol 2 (4) ◽  
pp. 425-439 ◽  
Author(s):  
A. Erdéyi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Small Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Boundary Value Problem ◽  
Image Position

In this paper we shall discuss the boundary value problem consisting of the nonlinear ordinary differential equation of the second order, and the boundary conditions.

On the Approximate Solutions of Heat-Conduction Problems

1963 ◽  
Vol 85 (3) ◽  
pp. 203-207 ◽  
Author(s):  
Fazil Erdogan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Approximate Solutions ◽  
Integral Transforms ◽  
Partial Differential ◽  
The Given

Integral transforms are used in the application of the weighted residual methods to the solution of problems in heat conduction. The procedure followed consists in reducing the given partial differential equation to an ordinary differential equation by successive applications of appropriate integral transforms, and finding its solution by using the weighted-residual methods. The undetermined coefficients contained in this solution are functions of transform variables. By inverting these functions the coefficients are obtained as functions of the actual variables.

A Numerical Procedure for Obtaining the Static and Pull-In Deflection and Voltage of Capacitive Microcantilever Beams

2006 ◽  
Author(s):  
Seyed Babak Ghaemi Oskouei ◽  
Aria Alasty
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Procedure ◽  
Nonlinear Ordinary Differential Equation ◽  
Static Deflection ◽  
Element Analysis ◽  
Fringing Field ◽  
Good Agreement

A numerical procedure is proposed for obtaining the static deflection, pull-in (PI) deflection and PI voltage of electrostatically excited capacitive microcantilever beams. The method is not time and memory consuming as Finite Element Analysis (FEA). Nonlinear ordinary differential equation of the static deflection of the beam is derived, w/wo considering the fringing field effects. The nondimensional parameters upon which PI voltage is dependent are then found. Thereafter, using the parameters and the numerical method, three closed form equations for pull-in voltage are developed. The results are in good agreement with others in literature.

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