This paper introduces two novel numerical algorithms for the efficient solution of coupled systems of nonlinear boundary value problems. The methods are benchmarked against existing methods by finding dual solutions of the highly nonlinear system of equations that model the flow of a viscoelastic liquid of Oldroyd-B type in a channel of infinite extent. The methods discussed here are the spectral relaxation method and spectral quasi-linearisation method. To verify the accuracy and efficiency of the proposed methods a comparative evaluation of the performance of the methods against established numerical techniques is given.
Visiting most, if not all, tourist destination of a country while visiting a country is an ideal plan of a tourist. In most cases if the tour is not carefully planned, it will be costly and time taking to travel between tourist destinations of a country. If we consider Ethiopia, a country which has been named as best tourism destination for 2015 by the European Council on Tourism and Trade (ECTT); there are many tourist destinations all over the country. The problem of determining the optimum route to visit all the tourist sites with minimum traveling time can be formulated as a travel salesman problem. In this study 17 of the famous tourist destination of Ethiopia will be selected and a travel salesman model will be formulated. Due to the NP hardness of the travel salesman problem, metaheuristic based algorithms are found to be more effective. Hence, a recently introduced swarm based metaheuristic algorithm, called prey predator algorithm will be used to deal with the formulated problem. The simulation result suggests that the best route to visit the selected destination is Addis Ababa ? Sof Omar Caves ? Bale Mountain National Park ? Abijiata-Shalla Lakes ? Netchisar National Park ? Mago National Park ? Omo National Park ? Gambella National Park ? Bahir Dar ? Lalibela ? Gonder ? Semien Mountain National Park ? Axum ? Ertale ? Yangudi Rassa National Park ? Awash National Park ? Harar ? Addis Ababa. It should be noted in some of the sites there is no direct route and hence a route through other cities is used and hence it should be recomputed in the future when a direct route between these tourist destinations is constructed.
Abstract. The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.Mathematical subject classification: Primary: 49Mxx; Secondary: 65Mxx.
Prey-predator algorithm (PPA) is a metaheuristic algorithm inspired by the interaction between a predator and its prey. In the algorithm, the worst performing solution, called the predator, works as an agent for exploration whereas the better performing solution, called the best prey, works as an agent for exploitation. In this paper, PPA is extended to a new version callednm-PPA by modifying the number of predators and also best preys. Innm-PPA, there will benbest preys andmpredators. Increasing the value ofnincreases the exploitation and increasing the value ofmincreases the exploration property of the algorithm. Hence, it is possible to adjust the degree of exploration and exploitation as needed by adjusting the values ofnandm. A guideline on setting parameter values will also be discussed along with a new way of measuring performance of an algorithm for multimodal problems. A simulation is also done to test the algorithm using well known eight benchmark problems of different properties and different dimensions ranging from two to twelve showing thatnm-PPA is found to be effective in achieving multiple solutions in multimodal problems and also has better ability to overcome being trapped in local optimal solutions.
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