Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

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.

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“…Moreover, the solution obtained by this lemma agrees with the published one, see Ref. [28] for details.…”

Section: Lemmasupporting

confidence: 88%

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

Ebaid

Alharbi

2020

PSIJ

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“…It was found that the results in the literature were recovered as special cases of the current ones. Furthermore, this work can be extended in the near future to deal with the recently published physical models [23][24][25].…”

Section: Resultsmentioning

confidence: 99%

Applicable Solution for a Class of Ordinary Differential Equations with Singularity

Ahamad

2020

ijaa

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Boundary value problems arise in many real applications such as nanofluids and other areas of applied sciences. The temperature/nanoparticles concentration are usually expressed as singular 2 ndorder ODEs. So, it is a challenge to obtain the exact solution of these problems due to the difficulty of the singularity encountered in the governing equations. By means of a suitable transformation, a direct approach is introduced to solve a general class of 2 nd-order ODEs. The efficiency of the obtained results is validated through selected problems in the literature. It is found that several existing solutions can be deduced as special cases of our generalized one. Moreover, the present results may be invested for similar future problems in fluid mechanics, especially nanofluids.

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“…Besides, several authors ([3]- [8]) implemented different analytical and numerical methods to treating the system (1)- (5). The LT method was widely applied to solve various physical models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. However, it requires massive calculations as seen in Refs.…”

Section: Introductionmentioning

confidence: 99%

A Simple Approach for Explicit Solution of The Neutron Diffusion Kinetic System

Al-Jeaid¹

2023

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This paper introduces a new approach to directly solve a system of two coupled partial differential equations (PDEs) subjected to physical conditions describing the diffusion kinetic problem with one delayed neutron precursor concentration in Cartesian geometry. In literature, many difficulties arise when dealing with the current model using various numerical/analytical approaches. Normally, mathematicians search for simple but effective methods to solve their physical models. This work aims to introduce a new approach to directly solve the model under investigation. The present approach suggests to transform the given PDEs to a system of linear ordinary differential equations (ODEs). The solution of this system of ODEs is obtained by a simple analytical procedure. In addition, the solution of the original system of PDEs is determined in explicit form. The main advantage of the current approach is that it avoided the use of any natural transformations such as the Laplace transform in the literature. It also gives the solution in a direct manner; hence, the massive computational work of other numerical/analytical approaches is avoided. Hence, the proposed method is effective and simpler than those previously published in the literature. Moreover, the proposed approach can be further extended and applied to solve other kinds of diffusion kinetic problems.

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Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

Cited by 15 publications

References 20 publications

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

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

Applicable Solution for a Class of Ordinary Differential Equations with Singularity

A Simple Approach for Explicit Solution of The Neutron Diffusion Kinetic System

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