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Numerical Solution of First Order Ordinary Differential Equation by Using Runge-Kutta Method
Issue:
Volume 6, Issue 1, March 2021
Pages:
1-8
Received:
20 December 2020
Accepted:
6 January 2021
Published:
10 March 2021
Abstract: In this paper, the classical fourth-order Runge-Kutta methodis presented for solving the first-order ordinary differential equation. First, the given solution domain is discretizedby using a uniform discretization grid point. Next by applyingthe forward difference method, we discretized the given ordinary differential equation. And formulating a difference equation. Then using this difference equation, the given first-order ordinary differential equation is solved by using the classicalfourth-order Runge-Kutta method at each specified grid point. To validate the applicability of the proposed method, two model examples are considered and solved at each specific grid point on its solution domain. The stability and convergent analysis of the present method is worked by supportedthe theoretical and mathematical statementsand the accuracy of the solution is obtained. The accuracy of the present methodhas been shown in the sense ofmaximumabsolute error and the local behavior of the solution is captured exactly. Numerical and exact solutions have been presented in tables and graphs and the corresponding maximumabsolute errorisalso presented in tables and graphs. The present method approximates the exact solution very well and it is quite efficient and practically well suitedfor solving first-order ordinary differential equations. The numerical result presented in tables and graphsindicates that the approximate solution is in good agreement with the exact solution. Hence the proposed method is accruable to solve ordinary differential equations.
Abstract: In this paper, the classical fourth-order Runge-Kutta methodis presented for solving the first-order ordinary differential equation. First, the given solution domain is discretizedby using a uniform discretization grid point. Next by applyingthe forward difference method, we discretized the given ordinary differential equation. And formulating a di...
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Challenges and Opportunities of Homegrown Ways of Peace Building: The Case of Gada System in Borana Community of Southern Ethiopia
Issue:
Volume 6, Issue 1, March 2021
Pages:
9-21
Received:
21 December 2020
Accepted:
21 January 2021
Published:
10 March 2021
Abstract: This study is concerned with challenges and opportunity of gada system in peacebuilding among Borana Oromo community of south Ethiopia. The objective of this paper was to assess the challenges and opportunities of the homegrown (gada system) in peacebuilding in Borana Oromo community. To achieve the objectives, a qualitative case study of research design was implemented. Members of gada council, gada leaders who are active in peacebuilding, concerned officials from Oromia and Borana culture and tourism office of government structure, knowledgeable elders of the Borana Oromo community were purposively selected as a sample of the study. Accordingly, in-depth interviews, key informant interviews, and focus group discussions were conducted. Data obtained by interviews and focus group discussion were analyzed and interpreted by applying relevant approaches to qualitative research. The findings show that there are challenges and opportunities in the practice of Gada system in peacebuilding. The politicization of gada leaders, religion, lack of budget for gada institution, low knowledge of gada systems are challenges of gada system in peacebuilding. On the other side, the gada system has the opportunity to maintain peace and bring peace and stability due to its nature that promotes democratic cultures and principles as its core values. In general, the study concludes that an effort of peacebuilding by gada system is effective to some extent requiring more actions to be done. The community is peacefully asking their question as compared to the past four years which is more violent without destruction of resources currently but this does not mean it brought a complete or lasting peace among the group rather show the system has its own contribution in building peace in the Borana zone.
Abstract: This study is concerned with challenges and opportunity of gada system in peacebuilding among Borana Oromo community of south Ethiopia. The objective of this paper was to assess the challenges and opportunities of the homegrown (gada system) in peacebuilding in Borana Oromo community. To achieve the objectives, a qualitative case study of research ...
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On a Reaction-Diffusion Model of COVID-19
Rebecca Walo Omana,
Issa Ramadhani Issa,
Francis-Didier Tshianyi Mwana Kalala
Issue:
Volume 6, Issue 1, March 2021
Pages:
22-34
Received:
23 November 2020
Accepted:
11 January 2021
Published:
26 March 2021
Abstract: Nowadays mathematical models play a major role in epidemiology since they can help in predicting the spreading and the evolution of diseases. Many of them are based on ODEs on the assumption that the populations being studied are homogenous sets of fixed points (individuals) but actually populations are far from being homogenous and people are constantly moving. In fact, thanks to science progresses, distances are no longer what they used to be in the past and a disease can travel and reach out even the most remote places on the globe in a matter of hours. HIV and Covid-19 outbreaks are perfect illustrations of how far and fast a disease can now spread. When it comes to studying the spatio-temporal spreading of a disease, instead of ODEs dynamic models the Reaction-Diffusion ones are best suited. They are inspired by the second Fick’s law in physics and are getting more and more used. In this article we make a study of the spatio-temporal spreading of the COVID-19. We first present our SEIR dynamic model, we find the two equilibrium points and an expression for the basic reproduction number (R0), we use the additive compound matrices and show that only one condition is necessary to show the local stability of the two equilibrium points instead of two like it is traditionally done, and we study the conditions for the DFE (Disease Free Equilibrium point) and the EE (Endemic Equilibrium point) to be globally asymptotically stable. Then we construct a diffusive model from our previous SEIR model, we investigate on the existence of a traveling wave connecting the two equilibrium thanks to the monotone iterative method and we give an expression for the minimal wave speed. Then in the last section we use the additive compound matrices to show that the DFE remains stable when diffusion is added whereas there will be appearance of Turing instability for the EE once diffusion is added. The conclusion of our article emphasizes the importance of barrier gestures and the fact that the more people are getting tested the better governments will be able to handle and tackle the spreading of the disease.
Abstract: Nowadays mathematical models play a major role in epidemiology since they can help in predicting the spreading and the evolution of diseases. Many of them are based on ODEs on the assumption that the populations being studied are homogenous sets of fixed points (individuals) but actually populations are far from being homogenous and people are cons...
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