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Analysis of the Properties of a Third Order Convergence Numerical Method Derived via the Transcendental Function of Exponential Form
Sunday Emmanuel Fadugba,
Jethro Olorunfemi Idowu
Issue:
Volume 5, Issue 4, December 2019
Pages:
97-103
Received:
14 September 2019
Accepted:
18 October 2019
Published:
4 November 2019
Abstract: This paper proposes a new numerical method for the solution of the Initial Value Problems (IVPs) of first order ordinary differential equations. The new scheme has been derived via the transcendental function of exponential type. The analysis of the properties of the method such as local truncation error, order of accuracy, consistency, stability and convergence were investigated. Two illustrative examples/test problems were solved successfully to test the accuracy, performance and suitability of the method in terms of the absolute relative errors computed at the final nodal point of the associated integration interval via MATLAB codes. It is observed that the method is found to be of third order convergence, consistent and stable. The numerical results obtained via the method agree with the exact solution. Moreover, it is also observed that the method is an improvement on Fadugba-Falodun scheme. Hence, the proposed numerical method is a good approach for solving the IVPs of various nature and characteristics in diverse areas of Ordinary Differential Equations (ODEs).
Abstract: This paper proposes a new numerical method for the solution of the Initial Value Problems (IVPs) of first order ordinary differential equations. The new scheme has been derived via the transcendental function of exponential type. The analysis of the properties of the method such as local truncation error, order of accuracy, consistency, stability a...
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Microscopic Manifestations of the Wave Nature and the Fifth Fundamental Field
Issue:
Volume 5, Issue 4, December 2019
Pages:
104-110
Received:
6 November 2019
Accepted:
23 November 2019
Published:
6 December 2019
Abstract: In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alternatives, like in Dirac unified formalism; when searching stationary solutions of the system vacuum-particle or the system vacuum-antiparticle. (ii) Considering the former, each spinner component shows the interaction of one particle charge with three vacuum fermions of spin-½; each oriented along one space direction. Furthermore, this allows deducting the triple nature of any gauge fermion. (iii) Each solution case is definable with a same wave front width. This determination became possible from the vector companion of that wave function one introduced before. Here, this points out the existence of transverse time. (iv) Both functions let emphasizing the existence of a third fundamental field of long range, which is identifiable to the fundamental spin field. (v) This unites the particle spin and orbital momenta and bears in addition a magnetic-like field, which is yet unknown. (vi) According to the charge, a particle field is observable in wave phenomena, from the manifestations of its gauge fermions or gauge bosons; when ejected from their stationary states by a perturbation… At last, the results highlight the quantum composition of wave functions, the spin-field patency, and the wave nature manifestation from five differentiable fields.
Abstract: In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alt...
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Numerical Analysis of Heat and Mass Transfer Flow of Nanofluid over a Moving Wedge Using Spectral Quasilinearization Method
Ayele Tulu,
Wubshet Ibrahim
Issue:
Volume 5, Issue 4, December 2019
Pages:
111-117
Received:
7 September 2019
Accepted:
28 October 2019
Published:
10 December 2019
Abstract: In this paper the problem of unsteady two-dimensional heat and mass transfer flow of nanofluid past a moving wedge is considered. The effects of nanoparticle volume fraction, viscous dissipation, chemical reaction, and convective boundary conditions are studied. The physical problem is modeled using partial differential equations. Using suitable similarity variables, the governing equations and their related boundary conditions are transformed into dimensionless forms of a system of coupled nonlinear ordinary differential equations. The resulting systems of equations are then solved numerically using spectral quasilinearization method (SQLM). The results reveal that the skin friction coefficient increases with increasing the values of nanoparticle volume fraction, unsteadiness and permeability parameters. The local Nusselt number reduces with increasing the value of nanoparticle volume fraction, Prandtl number and Eckert number. The local Sherwood number enhances with greater the value of nanoparticle volume fraction, unsteadiness, pressure gradient and chemical reaction parameters. Moreover, the method is checked against the previously published results and a very good agreement have been obtained.
Abstract: In this paper the problem of unsteady two-dimensional heat and mass transfer flow of nanofluid past a moving wedge is considered. The effects of nanoparticle volume fraction, viscous dissipation, chemical reaction, and convective boundary conditions are studied. The physical problem is modeled using partial differential equations. Using suitable si...
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Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity
Siaka Massou,
Alain Adomou,
Jonas Edou
Issue:
Volume 5, Issue 4, December 2019
Pages:
118-128
Received:
5 November 2019
Accepted:
28 November 2019
Published:
24 December 2019
Abstract: In this research work, we opt for the static spherical symmetric metric. Thus, taking into account the own gravitational field of elementary particles, we have obtained exact static spheric symmetric solutions of the nonlinear spinor and gravitational fields equations. The nonlinear terms in the spinor lagrangian density characterize the self-interaction of a spinor field. We have investigated in detail equations with power and polynomial nonlinearities. In this case, we have obtained exact regular solutions which have a localized energy density and limited total energy (soliton-like solutions) only if the mass parameter in the spinor field equations is equal to zero. In additional to this, the total charge and the total spin are bounded. We have also shown that in the linear case, soliton-like solutions are absent. But in the flat space-time, the obtained solutions are soliton-like configurations. Therefore, the proper gravitational field of elementary particles, the geometrical properties of the metric and the nonlinear terms in the lagrangian density play a crucial role in the purpose to get the regular solutions with localized energy density and limited total energy.
Abstract: In this research work, we opt for the static spherical symmetric metric. Thus, taking into account the own gravitational field of elementary particles, we have obtained exact static spheric symmetric solutions of the nonlinear spinor and gravitational fields equations. The nonlinear terms in the spinor lagrangian density characterize the self-inter...
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