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The N-Point Definite Integral Approximation Formula (N-POINT DIAF)
Francis Oketch Ochieng’,
Nicholas Muthama Mutua,
Nicholas Mwilu Mutothya
Issue:
Volume 6, Issue 1, February 2017
Pages:
1-33
Received:
20 November 2016
Accepted:
26 December 2016
Published:
21 February 2017
Abstract: Various authors have discovered formulae for numerical integration approximation. However these formulae always result to some amount of error which may differ in size depending on the formula. It’s therefore important that a formula with highest precision has been discovered and should be implemented for use in numerical integration approximations problems, especially for the definite integrals which cannot be evaluated by applying the analytical techniques. The present paper therefore explores the derivation of the N-point Definite Integral Approximation Formula (N-point DIAF) which amounts to the discovery of the 2-Point DIAF. This formula will assist in almost accurate evaluation of all definite integrals numerically. The proof of the formula is given, a specific test problem is then solved using the discovered 2-Point DIAF to obtain the solution numerically, which has the highest precision compared to other numerical methods of integration. Further the error terms are obtained and compared with the existing methods. Finally, the effectiveness of the proposed formula is illustrated by means of a numerical example.
Abstract: Various authors have discovered formulae for numerical integration approximation. However these formulae always result to some amount of error which may differ in size depending on the formula. It’s therefore important that a formula with highest precision has been discovered and should be implemented for use in numerical integration approximations...
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Double-Diffusion MHD Free Convective Flow along a Sphere in the Presence of a Homogeneous Chemical Reaction and Soret and Dufour Effects
A. J. Chamkha,
A. M. Aly,
Z. A. S. Raizah
Issue:
Volume 6, Issue 1, February 2017
Pages:
34-44
Received:
5 January 2017
Accepted:
19 January 2017
Published:
23 February 2017
Abstract: A numerical solution is presented for the effects of chemical reaction, thermal radiation, Soret number, Dufour number and magnetic field on double-diffusion free convection flow along a sphere. The governing boundary-layer equations of the problem are formulated and transformed into non-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. The Roseland approximation is used to describe the radiative heat flux in the energy equation. Representative results for the fluid velocity, temperature and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.
Abstract: A numerical solution is presented for the effects of chemical reaction, thermal radiation, Soret number, Dufour number and magnetic field on double-diffusion free convection flow along a sphere. The governing boundary-layer equations of the problem are formulated and transformed into non-similar form. The obtained equations are solved numerically b...
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Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property
Zhudeng Wang,
Yuan Wang,
Keming Tang
Issue:
Volume 6, Issue 1, February 2017
Pages:
45-53
Received:
8 January 2017
Accepted:
19 January 2017
Published:
23 February 2017
Abstract: We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left (right)-conjunctive left (right) arbitrary ˅-distributive left (right) semi-uninorms and lower approximation right arbitrary ˄-distributive implications which satisfy the order property.
Abstract: We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationsh...
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Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model
Akaninyene D. Antia,
Okon P. Akpan
Issue:
Volume 6, Issue 1, February 2017
Pages:
54-59
Received:
23 November 2016
Accepted:
21 January 2017
Published:
24 February 2017
Abstract: In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.
Abstract: In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle depe...
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Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate
N. M. Ridwan Zahed,
Md. Yeakub Ali,
Md. Jashim Uddin,
Mohammed Nasir Uddin
Issue:
Volume 6, Issue 1, February 2017
Pages:
60-67
Received:
21 January 2017
Accepted:
6 February 2017
Published:
4 March 2017
Abstract: In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.
Abstract: In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear...
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