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Thermal Conductivity Equations via the Improved Adomian Decomposition Methods
Issue:
Volume 9, Issue 3, June 2020
Pages:
30-55
Received:
1 April 2020
Accepted:
11 May 2020
Published:
27 May 2020
Abstract: Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.
Abstract: Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and ...
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The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations
Issue:
Volume 9, Issue 3, June 2020
Pages:
56-63
Received:
18 April 2020
Accepted:
12 May 2020
Published:
27 May 2020
Abstract: In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G2-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.
Abstract: In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’...
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Approximating Solutions of Non Linear First Order Abstract Measure Differential Equations by Using Dhage Iteration Method
Dnyanoba Maroti Suryawanshi,
Sidheshwar Sangram Bellale,
Pratiksha Prakash Lenekar
Issue:
Volume 9, Issue 3, June 2020
Pages:
64-69
Received:
15 April 2020
Accepted:
30 April 2020
Published:
4 June 2020
Abstract: In this paper we have proved the approximating solutions of the nonlinear first order abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability of given results in the paper. Sharma [2] initiated the study of nonlinear abstract differential equations and some basic results concerning the existence of solutions for such equations. Later, such equations were studied by various authors for different aspects of the solutions under continuous and discontinuous nonlinearities. The study of fixed point theorem for contraction mappings in partial ordered metric space is initiated by different authors. The study of hybrid fixed point theorem in partially ordered metric space is initiated by Dhage with applications to nonlinear differential and integral equations. The iteration method is also embodied in hybrid fixed point theorem in partially ordered spaces by Dhage [12]. The Dhage iteration method is a powerful tool for proving the existence and approximating results for nonlinear measure differential equations. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. In this paper we adopted this iteration method technique for abstract measure differential equations.
Abstract: In this paper we have proved the approximating solutions of the nonlinear first order abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability o...
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Mathematical Model and Optimal Control of New-Castle Disease (ND)
Uwakwe Joy Ijeoma,
Inyama Simeon Chioma,
Omame Andrew
Issue:
Volume 9, Issue 3, June 2020
Pages:
70-84
Received:
9 December 2019
Accepted:
10 January 2020
Published:
4 June 2020
Abstract: We formulated a five compartmental model of ND for both the ordinary and control models. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the disease-free equilibrium (DFE) and endemic equilibrium were proved using Lyponav method. We went further to carry out the sensitivity analysis or parametric dependence on R0 and later formulated the optimal control problem. We finally looked at numerical Results on poultry productivity in the presence of Infectious Newcastle Disease (ND) and we drew six graphs to demonstrate this. We observe that in absence of any control measure, the number of latently infected birds will increase rapidly from the initial population size of 80 to 160 birds within 1-3 days, whereas in the presence of control measures the population size will reduces to about 30 birds and goes to a stable state. This shows that the control measures are effective. The effect of the three control measures on the infectious classes can be seen. The number of non-productive infectious birds reduces to zero with control whereas the number of infectious productive reduces to about 8 birds and goes to its stable state when control is applied. This shows that the application of all three control measures tends to be more effective in the non- productive infectious bird population. It was also establish that the combination of efficient vaccination therapy and optimal efficacy of the vaccines are significantly more effective in the infectious productive birds’ population, since the combination reduces the population size of the birds to zero with 9–10 days. From the simulation also we see that optimal efficacy of the vaccine and effort to increase the number of recovered birds increases the number of latently infected birds population to about 129 at the early days of the infection whereas from another graph, the infectious productive birds reduces to 15 while the non -productive birds reduces to zero. The results from the simulation also show clearly, the effect of vaccination therapy on the latently infected birds. We observe that this programme will reduce the number of latently infected birds even if it not done more often. From the simulation, we further observe that this programme has effect on the infectious classes especially the non-productive infectious bird population, which reduces to zero after about 4 days.
Abstract: We formulated a five compartmental model of ND for both the ordinary and control models. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the...
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Heuristic Algorithms of Coincidence for the Estimation of Movements in Compression of Images
Fernando José Hernández Gómez
Issue:
Volume 9, Issue 3, June 2020
Pages:
85-95
Received:
14 September 2019
Accepted:
25 May 2020
Published:
8 June 2020
Abstract: The NP-Completeness theory states that exact and efficient algorithms are unlikely to exist for the class of NP-difficult problems. One way to deal with NP hardness is to relax the optimality requirement and look for solutions instead that are close to the optimum. This is the main idea behind the approximation algorithms, which are called heuristic or metaheuristic. The problem of motion estimation is a process with a high degree of computational complexity, it requires sufficient memory space and execution time. It represents the cost of static, dynamic and video image sequence coding. The main task is to minimize the distortion rate and improve visual quality. This makes research in the field of coding, image compression and video focus on finding efficient algorithms to carry out the estimation of movement in a reasonable time. If a list of images of n elements is analyzed, there are feasible solutions. So, an exhaustive search is too slow, even for small values of the solution space. Therefore, from a practical point of view, it is crucial to have efficient and fast heuristic algorithms that avoid thorough search. In this investigation we design and implement heuristic algorithms, based on the frequency domain, which are applied on the coefficients of the discrete transform of the cosine and wavelets. Also, we propose temporal domain algorithms such as block-matching algorithms, which focus your search on the maximum coincidence of the current image with the reference one. The algorithms used during the implementation of this research work were written with the mathematical programming language MATLAB. In addition, we review the basic concepts of image processing, video, compression algorithms and motion estimation frequently used. The evaluation of the algorithms was carried out with a set of images provided by a previous acquisition system. We show the improvement of visual quality, the amount of compressed or reconstructed information and the behavior of the methods in the search for similarities between pixels or images. Finally, we contribute to the dissemination of new lines of scientific research that lead to the expansion and improvement of the study, the generation of new knowledge, since it is a young area within the Education discipline of Nicaragua.
Abstract: The NP-Completeness theory states that exact and efficient algorithms are unlikely to exist for the class of NP-difficult problems. One way to deal with NP hardness is to relax the optimality requirement and look for solutions instead that are close to the optimum. This is the main idea behind the approximation algorithms, which are called heuristi...
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Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change
Bazuaye Frank Etin-Osa,
Ijomah Maxwell Azubike
Issue:
Volume 9, Issue 3, June 2020
Pages:
96-101
Received:
3 October 2019
Accepted:
26 May 2020
Published:
8 June 2020
Abstract: Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.
Abstract: Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing ...
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Some Metric Properties of Semi-Regular Equilateral Nonagons
Issue:
Volume 9, Issue 3, June 2020
Pages:
102-107
Received:
14 May 2020
Accepted:
2 June 2020
Published:
17 June 2020
Abstract: A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). Unlike regular polygons, one characteristic element is not enough to analyze the metric properties of semi-regular polygons, and an additional one is needed. To select this additional characteristic element, note that the following regular triangles can be inscribed to a semi-regular equilateral nonagon by joining vertices: ∆A1 A4A7, △ A2 A5 A8, △A3 A6 A9. Now have a look at triangle △A1 A4A7. Let us use the mark φ=∡(a,b1) to mark the angle between side a of the semi-regular nonagon and side b1 of the inscribed regular triangle. In interpreting the metric properties of a semi-regular equilateral nonagon, in addition to its side, we also use the angle that such side creates with the side of one of the three regular triangles that can be inscribed to such semi-regular nonagon. We consider the way in which convexity, possibility of construction, surface area, and other properties depend on a side of the semi-regular nonagon and angle φ=∡(a,b1).
Abstract: A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different s...
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