A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations

In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.  Keywords: Power series, Collocation, Interpolation, Block method, Stiff

Eighth order Predictor-Corrector Method to Solve Quadratic Riccati Differential Equations

In this paper, the eighth-order predictor-corrector method is presented for solving quadratic Riccati differential equations. First, the interval is discretized and then the method is formulated by using Newton’s backward difference interpolation formula. The stability and convergence of the method have been investigated. To validate the applicability of the proposed method, two model examples with exact solutions have been considered and numerically solved. Maximum absolute errors are presented in tables and figures for different values of mesh size h and the present method gives better results than some existing numerical methods reported in the literature. &nbsp

The role of off-grid energy systems for sustainable energy transition in Ethiopia

The lack of energy in rural areas of Ethiopia, the second-most populous country in Africa, impedes development, and economic growth. Nonetheless, the nation has been working hard to create a green legacy and use renewable energy. Due to restricted access to national energy supplies, traditional fuels like fuel wood, dung cakes, and agricultural residues are primarily used for cooking and lighting in Ethiopia. Solar, hydro, wind, and geothermal energy are among the many renewable energy sources that exist but are not yet used. Grid and off-grid energy systems can be combined to accomplish this transition. The renewable energy-based off-grid system lowers greenhouse gas emissions, lessens the use of conventional fuels, enhances indoor air quality, and protects the ecosystem. To better understand how off-grid energy systems can support Ethiopia's energy transition, this paper analyzes the country's current energy situation, highlights the role of off-grid solutions, and suggests strategies to increase their adoption and spread. To achieve this, it examines the obligations, advantages, and difficulties associated with putting off-grid energy solutions into practice during Ethiopia's energy transition. The paper addresses the following questions: How can off-grid energy systems contribute to Ethiopia's energy transition? What are the benefits of off-grid solutions? What are the responsibilities, opportunities, and challenges associated with implementing off-grid energy systems in Ethiopia? What is the implication of the national energy policy and regulatory frameworks? How can the adoption and expansion of off-grid energy systems be boosted? The results showed that off-grid energy systems, particularly those far from the national grid, are promising solutions to Ethiopia's energy issues. These systems can facilitate the nation's overall energy transition, enhance access to energy, and promote sustainability. Off-grid energy systems can help achieve several SDGs ((SDG 5, SDG 1, SDG 7, SDGs 3 and 4, and SDG 13). However, because of insufficient funding, ineffective laws and regulations, and low stakeholder commitment, the development of off-grid energy systems is moving more slowly than anticipated. To promote investments in off-grid energy, the government, business community, and international organisations must collaborate to develop off-grid energy systems in Ethiopia. Addressing major obstacles and putting laws, rules, and incentives that benefit the whole off-grid ecosystem from importers to consumers will help hasten the energy transition. To do this rules that enable and guarantee the use of all available implementing agent’s public, private, public-private partnerships, and cooperatives must be established and enforced

Development of alternative fuel for cement industries: The case of Messebo cement factory in Ethiopia.

The cement industry is struggling with dwindling fossil fuel resources and environmental issues related to climate change. This sector is known for its high energy consumption and generates significant CO2 emissions, accounting for 19% of global thermal energy consumption and 7% of CO2 emissions. For this reason, Cement industries are seeking to replace traditional energy sources with alternative fuels. This study aims to investigate and optimize alternative fuels, evaluating their chemical and physical properties, energy output, production capacity, effect on clinker quality, and impact on combustion flue gas emissions. The study shows that the alternative fuels meet or exceed the minimum international standard of 14 MJ/kg for net calorific value. Therefore, they could replace up to 40% of South African coal in the clinker pre-calcining process. Using alternative fuels such as P. j wood, P. j leaf, P. j charcoal, used tire, and optimized fuels could potentially reduce CO2 emissions by 2%, 9%, 9%, 21%, and 17% respectively. Therefore, policy makers and companies should strongly consider adopting these recommended alternatives

Investigating the soil-maresha plough interaction using a mobile, in-situ testing device

The ard plough – maresha dates from antiquity and is used in Ethiopia. The Maresha is a non-inverting tillage tool consisting of a steel-tipped tine attached to a draught pole at an adjustable shallow angle. It has narrow side-wings, attached to the left and right side of it, to push soil to either side. Most work on the interaction between soil and maresha is documented as trial-and-error procedures based on experience in a cultural context. In experimental research on the maresha plough, challenges arise from uneven oxen strength along with different pace of walking, uncontrolled implement behaviour, and rough field conditions. No research has ever systematically investigated the link between the maresha plough and soil characteristics. There is a lack of information on the effect of maresha’s side-wings and tillage angle on draught requirement and soil loosening. The aim of this research was to investigate the soil-maresha plough interaction and, more specifically, the effect of tillage angle and side-wings on draught and soil loosening. In this study a mobile soil bin facility was developed as an in-situ testing device. The developed soil bin has three rows (track-rails) with four rail lines - for three parallel experimental lines. The easy disassembly and relocation of the rails make that the testing device can be moved around a terrain or between fields, depending on the experimental requirements. The instrumentation and data acquisition system was mounted on a carriage and included load cells, linear variable displacement transducers (LVDT), and an optical encoder. The design parameters for the experiments were: (1) tool geometry - winged and wingless maresha, and (2) rake angles (for shallow, medium deep, and deep, representing primary, secondary, and tertiary tillage processes in Ethiopia, respectively). The operating parameters were tool travel speed and tillage depth. The experimental soil was classified as Vertisol. The additional variables were furrow area, moisture content, bulk density, rock fragments, and penetrometer resistance. The winged maresha plough has a greater contact with the moving soil than its wingless counterpart. Here the draught was expected to increase with contact area, as adhesion and friction resistance increases with area. However, results showed that the winged maresha plough required lower draught than wingless maresha. The side-wings stimulate in these soils most likely the crack propagation by a wedging effect and thereby enhance and facilitate subsequent ploughing by reducing the soil resistance ahead of the ploughshare. Results showed that draught increased with rake angle as could be expected. Similarly, an increased operating depth had a positive correlation with draught requirement. Experimental limitations and difficulties came from the use of a walking tractor as pulling source. Under some conditions variability in soil surface and soil cover by plants can cause variable wheel slippage resulting in a change in pulling force and changing travel speed. Experimental runs also encountered difficulties in fields with large buried rock fragments as these would stop the forward movement and sometimes caused damage to the tool. This is in line with farmers’ actions to remove bigger rock fragments from the field. On the other hand, it was found that the presence of small rock fragments in the soil tends to reduce draught requirement with higher tool travel speed and facilitate tillage. Again this is in line with the reluctance of farmers to take away the smaller rock fragments (i.e. < 5 cm across) from their fields, since they also believe these benefit soil moisture conservation and protect topsoil from erosion. The penetrometer recording showed the presence of a plough pan at depth between 10 and 15 cm below the soil surface. This emphasises the need to locally destroy the plough pan by occasional deep ploughing. The developed soil bin facility can be used as a platform for controlled experiments with different tillage tool geometry types to get information on how geometry affects draught and soil manipulation. Since the facility is mobile and allows in-field experimentation it can be used in different types of soils for tillage tool studies. Further, with minor alterations, the system can also be used in soil-wheel interaction (traction) studies.status: publishe

Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms

Abstract In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results

Ethiopia needs peace to accelerate its SDG 7 achievements

Ethiopia has been striving to achieve its SDG 7 targets by heavily investing in the power sector. Large-scale dams have been developed and are currently under construction, including the Grand Ethiopian Renaissance Dam (GERD). These developments have supported the expansion of connectivity to millions of people. However, due to political differences between the Ethiopian federal government and the Tigray regional government, a devastating war broke out in November 2020, and the conflict has since expanded to other regions of Ethiopia. These conflicts have hindered Ethiopia's economic development, derailing achievements of the SDG 7 targets. The negotiated peace settlement that was signed in Pretoria and Nairobi is encouraging and should be sustained. The government must use this opportunity and commit the country's resources to the rehabilitation of damaged critical infrastructure and initiating large-scale projects to promote lasting peace by building confidence in the population. The conflicts of the last two years should be used as a lesson for Ethiopians to resolve political differences through constructive and equitable dialogue across the political spectrum. We need to develop a culture of resolving differences by ourselves through a) strengthening institutions and norms to nurture a political culture of resolving political differences through dialogues; b) developing and strengthening an independent judicial system; c) developing a culture of providing justice for those affected and introducing a true reconciliation process; and d) developing mechanisms to ensure and protect critical infrastructures during conflicts

Characterization of Municipal Solid waste’s Potential for Power Generation at Mekelle City as a Waste Minimisation strategy

Waste to energy concept is one of the best methods, which not only consider the environment but also generate energy from municipal solid waste (MSW). Generation of MSWs at Mekelle city, Ethiopia, has grown steadily mainly due to migration of people from rural areas. However, the waste has not been managed and utilised as a useful resource due to lack of awareness and proper technology in the city. The objective of this study was to measure the heat content of solid waste generated in the city. Measurement of heating value was performed on collected samples using bomb calorimeter and Dulong’s formula. The average heating values obtained from the experimental analysis were 17,001 kJ/kg. The energy content obtained from the elemental composition of waste using Dulong’s formula was 16,853 kJ/kg. These results indicate that it could be possible to generate 8.7 MW of power from the solid waste composition represented by the sample; it is a good potential to alleviating the power shortage and interruption problems in the city. The results of this study could be used for design considerations in the selection and establishment of waste to energy technology in Mekelle city