scholarly journals Applications of a Generalized Singular Boundary Value Problem for the Exact Solutions of Some Temperature/Concentration Equations

2020 ◽  
pp. 1-9
Author(s):  
Abdelhalim Ebaid ◽  
Fahad M. Alharbi
Keyword(s):  
Fluid Mechanics ◽  
Boundary Value ◽  
Analytic Solutions ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Governing Equations ◽  
Special Cases ◽  
Nanoparticles Concentration ◽  
Theoretical Results

In the field of fluid mechanics, the temperature distribution and the nanoparticles concentration are usually described by singular boundary value problems (SBVPs). Such SBVPs are also used to describe various models with applications in engineering and other areas. Generally, obtaining the analytic solutions of such kind of problems is a challenge due to the singularity involved in the governing equations. In this paper, a class of SBVPs is analyzed. The solution of this class is analyzed and investigated through developing several theorems and lemmas. In addition, the theoretical results are invested to construct several solutions for various models/problems in fluid mechanics in the literature. Moreover, the published results are recovered as special cases of our analysis.

scholarly journals Conditions for the solvability of singular boundary value problems

1996 ◽  
Vol 53 (3) ◽  
pp. 485-497
Author(s):  
Xiyu Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Necessary And Sufficient Conditions ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Necessary And Sufficient

Consider the singular boundary value problem (r(x′))′ + f(t, x) = 0, 0 < t < 1. We give necessary and sufficient conditions for this problem to have solutions. In addition, a uniqueness result is obtained.

scholarly journals POSITIVE SOLUTIONS FOR NON-RESONANT SINGULAR BOUNDARY-VALUE PROBLEMS WITH A LINEAR TERM

2007 ◽  
Vol 50 (1) ◽  
pp. 217-228 ◽  
Author(s):  
Haishen Lü ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Linear Term ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems

AbstractThis paper presents new existence results for the singular boundary-value problem\begin{gather*} -u''+p(t)u=f(t,u),\quad t\in(0,1),\\ u(0)=0=u(1). \end{gather*}In particular, our nonlinearity $f$ may be singular at $t=0,1$ and $u=0$.

scholarly journals On a Constructive Approach for Derivative-Dependent Singular Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
R. K. Pandey ◽  
Amit K. Verma
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Constructive Approach

We present a constructive approach to establish existence and uniqueness of solution of singular boundary value problem-(p(x)y′(x))′=q(x)f(x,y,py′)for0<x≤b,y(0)=a,α1y(b)+β1p(b)y′(b)=γ1.Herep(x)>0on(0,b)allowingp(0)=0. Furtherq(x)may be allowed to have integrable discontinuity atx=0, so the problem may be doubly singular.

scholarly journals Existence theory for nonresonant singular boundary value problems

1995 ◽  
Vol 38 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Trivial Solution ◽  
Boundary Value ◽  
Existence Results ◽  
Existence Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems

We present some existence results for the “nonresonant” singular boundary value problem a.e. on [0, 1] with Here μ is such that a.e. on [0, 1] with has only the trivial solution.

scholarly journals Singular boundary value problem on infinite time scale

2006 ◽  
Vol 2006 ◽  
pp. 1-13
Author(s):  
Zhao-Cai Hao ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Approximation Method ◽  
Time Scale ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Infinite Time

This paper deals with a class of singular boundary value problems of differential equations on infinite time scale. An existence theorem of positive solutions is established by using the Schauder fixed point theorem and perturbation and operator approximation method, which resolves the singularity successfully and differs from those of some papers. In the end of the paper, an example is given to illustrate our main result.

scholarly journals A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
R. K. Pandey ◽  
G. K. Gupta
Keyword(s):  
Singular Point ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Boundary Value ◽  
Uniform Mesh ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Order Method ◽  
Singular Boundary Value Problems ◽  
Fourth Order Method

We present a fourth order finite difference method for doubly singular boundary value problem (p(x)y′(x))′=q(x)f(x,y),  0<x  ≤1 with boundary conditions y(0)=A (or  y'(0)=0  or  limx→0p(x)y'(x)=0) and αy(1)+ βy'(1)=γ, where α(>0),  β(≥0),  γ and A are finite constants. Here p(0)=0 and q(x) is allowed to be discontinuous at the singular point x=0. The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.

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