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Higher-Order Numerical Method for Singularly Perturbed Delay Reaction-Diffusion Problems
Gemechis File Duressa,
Tesfaye Aga Bullo
Issue:
Volume 10, Issue 3, June 2021
Pages:
68-76
Received:
18 May 2021
Accepted:
2 July 2021
Published:
9 July 2021
Abstract: In this paper, a higher-order numerical method is presented for solving the singularly perturbed delay differential equations. Such kind of equations have a delay parameter on reaction term and exhibits twin boundary layers or oscillatory behavior. Recently, different numerical methods have been developed to solve the singularly perturbed delay reaction-diffusion problems. However, the obtained accuracy and its rate of convergence are satisfactory. Thus, to solve the considered problem with more satisfactory accuracy and a higher rate of convergence, the higher-order numerical method is presented. First, the given singularly perturbed delay differential equation is transformed to asymptotically equivalent singularly perturbed two-point boundary value convection-diffusion differential equation by using Taylor series approximations. Then, the constructed singularly perturbed boundary value differential equation is replaced by three-term recurrence relation finite difference approximations. The Richardson extrapolation technique is applied to accelerate the fourth-order convergent of the developed method to the sixth-order convergent. The consistency and stability of the formulated method have been investigated very well to guarantee the convergence of the method. The rate of convergence for both the theoretical and numerical have been proven and are observed to be in accord with each other. To demonstrate the efficiency of the method, different model examples have been considered and simulation of numerical results have been presented by using MATLAB software. Numerical experimentation has been done and the results are presented for different values of the parameters. Further, The obtained numerical results described that the finding of the present method is more accurate than the findings of some methods discussed in the literature.
Abstract: In this paper, a higher-order numerical method is presented for solving the singularly perturbed delay differential equations. Such kind of equations have a delay parameter on reaction term and exhibits twin boundary layers or oscillatory behavior. Recently, different numerical methods have been developed to solve the singularly perturbed delay rea...
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Assessment Practices of Secondary School Mathematics Teachers in Guraghe Zone
Lemi Moges Mengesha,
Solomon Zerfu Degefa
Issue:
Volume 10, Issue 3, June 2021
Pages:
77-83
Received:
7 June 2021
Accepted:
16 July 2021
Published:
27 July 2021
Abstract: This paper was intended to examine mathematics teacher’s practices of assessment techniques used in secondary schools in Guraghe Zone and attempt to explore methods of assessment used by mathematics teachers, nature of feedback provided to student and the support provided by school authorities to enable them undertake assessment effectively. For this study, mixed research approach, inferential statistics and descriptive survey method would be employed; both quantitative and qualitative data were gathered through questionnaire, document analysis, FGD and interviews. The total sample sizes of the study were 377 students and all mathematics teachers in the selected schools. In addition thirteen school principals were interviewed. In the selection of the sample population, stratified sampling, systematic random sampling and purposive samplings were used. Thus, the findings indicate that, the overall respondents’ perception towards practices of continuous assessment has mean 3.630 and standard deviation 1.063 which is medium perception. In addition to this, the result showed that the first challenging step to implement Continuous assessment is large class size; the second is lack of in-services training, the third is it takes time and the last challenging step is shortage of teaching materials. Study showed that most of the teachers use the traditional feedback mechanism for continuous assessment which is not recommendable and had to use the enhanced feedback to encourage the learners’ capacity. So, concerned bodies of the zone education office and schools should give support by providing teaching materials and giving training for teachers in order to increase and develop their assessment practices in theimplementation Continuous assessment.
Abstract: This paper was intended to examine mathematics teacher’s practices of assessment techniques used in secondary schools in Guraghe Zone and attempt to explore methods of assessment used by mathematics teachers, nature of feedback provided to student and the support provided by school authorities to enable them undertake assessment effectively. For th...
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Minimum Degree Distance of Five Cyclic Graphs
Nadia Khan,
Munazza Shamus,
Fauzia Ghulam Hussain,
Mansoor Iqbal
Issue:
Volume 10, Issue 3, June 2021
Pages:
84-88
Received:
26 May 2021
Accepted:
28 July 2021
Published:
4 August 2021
Abstract: Let G be a connected graph with n vertices. Then the class of connected graphs having n vertices is denoted by Gn. The subclass of connected graphs with 5 cycles are denoted by Gn5. The classification of graph G∈Gn5 depends on the number of edges and the sum of the degrees of the vertices of the graph. Any graph in Gn5 contains five linearly independent cycles having at least n+3 edges and the sum of degrees of vertices of 5-cyclic must be equal to twice of n+4. In this paper, minimum degree distance of class of five cyclic connected graph is investigated. To find minimum degree distance of a graph some transformations T have been defined. These transformation have been applied on the graph G∈Gn5 in such a way that the resultant graph belongs to Gn5 and also degree distance of T(G) is always must be less than G. For n=5, the five 5-cyclic graph has minimum degree distance 78 and the minimum degree distance of 5-cyclic graphs having six vertices is 124. In case of n greater than 6, a general formula for minimum degree distance is investigated. In this paper, we proved that the minimum degree distance of connected 5 cyclic graphs is 3n2+13n-62 by using transformations, for n≥7.
Abstract: Let G be a connected graph with n vertices. Then the class of connected graphs having n vertices is denoted by Gn. The subclass of connected graphs with 5 cycles are denoted by Gn5. The classification of graph G∈Gn5 depends on the number of edges and the sum of the degrees of the vertices of the graph. Any graph in Gn5 contains five linearly indepe...
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