The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study

Ebaid, Abdelhalim; Alharbi, Weam; Aljoufi, Mona D.; El‐Zahar, Essam R.

doi:10.3390/math8101726

Cited by 13 publications

(8 citation statements)

References 13 publications

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“…As indicated in section 2, the solution of the present problem depends on the solution of the system ( 16)- (17). To find such solution, we just compare between the system ( 16)-( 17) and the system ( 18)- (19) to assign the values of a, b, c, and d. By this, we have…”

Section: Closed-form Series Solutionmentioning

confidence: 99%

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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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Section: Closed-form Series Solutionmentioning

confidence: 99%

“…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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“…al 9 solved a general class of SBVPs with applications in nanofulids via the LT. Bakodah and Ebaid 10 addressed the Ambartsumian delay equation using the LT. A variety of other of LT applications in addition to other transforms can be found in Refs. 11 – 30 . In this paper we consider the application of the LT for the solution of the system ( 1 )–( 4 ).…”

Section: Introductionmentioning

confidence: 99%

On solving the chlorine transport model via Laplace transform

Aljohani

Ebaid

Algehyne

et al. 2022

Sci Rep

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This paper analyzes the two-dimensional chlorine-transport model in pipes. The studied model is in the form of a second-order partial differential equation with a set of boundary conditions. Obtaining exact solution for the current model is a challenge due to the nature of the involved boundary conditions, especially, when applying the Laplace transform. However, such difficulties are solved via implementing the method of residues. The exact solution is obtained in terms of the Bessel functions. The expression for a dimensionless cup-mixing average concentration is also derived analytically. The proposed approach is validated via numerical examples for comparing the results with those in the literature. The present analysis/approach is effective/straightforward and can be further applied on other similar models under different boundary conditions.

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“…Although the LT method was shown as an effective and efficient approach to solve several scientific models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], it needs massive computational calculations when applied on the present system, especially when using the residues method as can be observed in Khaled [2], Bakodah and Ebaid [16], and Ebaid et al [20]. However, researchers in the field of Mathematics and Physics would prefer simple but effective methods to solve the governing system of the studied phenomena.…”

Section: Introductionmentioning

confidence: 99%

A Novel Ansatz Method for Solving the Neutron Diffusion System in Cartesian Geometry

Al-Sharif

Ebaid

Alrashdi

et al. 2022

JAMCS

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This paper analyzes the system of partial differential equations (PDEs) describing the diffusion kinetic problem with one delayed neutron precursor concentration in Cartesian geometry. The neutron diffusion kinetic equation is a popular problem in the fundamental Physics which is of practical applications in both nuclear physics and reactor design. For safety considerations, accurate solution of the this fundamental problem is required and mandatory. However, many difficulties arise when dealing with the current model using various numerical/analytical approaches as can be noticed in the literature. So, it is the objective of this paper to develop a new ansatz method to directly solve such fundamental model. It is shown in this work that our approach is straightforward and simpler when compared with other approaches in the relevant literature.

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The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study

Cited by 13 publications

References 13 publications

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

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

On solving the chlorine transport model via Laplace transform

A Novel Ansatz Method for Solving the Neutron Diffusion System in Cartesian Geometry

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