Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicit...Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.展开更多
When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The q...When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.展开更多
为简化工业机器人逆运动学求解过程,提高求解精度,增强求解算法通用性,提出一种计算工业机器人逆运动学问题的混合优化算法(hybrid optimization algorithm,HOA)。该方法基于冯诺依曼邻域和差分进化算法对标准灰狼优化算法(grey wolf op...为简化工业机器人逆运动学求解过程,提高求解精度,增强求解算法通用性,提出一种计算工业机器人逆运动学问题的混合优化算法(hybrid optimization algorithm,HOA)。该方法基于冯诺依曼邻域和差分进化算法对标准灰狼优化算法(grey wolf optimize,GWO)的种群个体进行重新构造,得到一种改进的GWO;在Rosenbrock搜索法中引入柯西变异改善劣质解;将改进的GWO的解作为Rosenbrock搜索法的初值计算运动学逆解,以六自由度和七自由度工业机器人为测试对象进行仿真实验。结果表明,混合优化算法相较于对比算法具有更高的精度,更好的稳定性和通用性,证明了算法的有效性。展开更多
In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studie...In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both discretization techniques approximate correctly solution of advection equation and compare their accuracy and performance.展开更多
Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the ...Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the stability conditions for second order wave equation with central difference temporal discretization.The shape parameter of the radial basis functions not only has strong influence on the spatial stability and accuracy,but also has profound influence on the temporal stability.Numerical studies are conducted and show reasonable agreement with stability analysis.Conclusions of selecting shape parameters as well as spatial discretization for solution stability are also presented.展开更多
文摘Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.
文摘When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.
文摘为简化工业机器人逆运动学求解过程,提高求解精度,增强求解算法通用性,提出一种计算工业机器人逆运动学问题的混合优化算法(hybrid optimization algorithm,HOA)。该方法基于冯诺依曼邻域和差分进化算法对标准灰狼优化算法(grey wolf optimize,GWO)的种群个体进行重新构造,得到一种改进的GWO;在Rosenbrock搜索法中引入柯西变异改善劣质解;将改进的GWO的解作为Rosenbrock搜索法的初值计算运动学逆解,以六自由度和七自由度工业机器人为测试对象进行仿真实验。结果表明,混合优化算法相较于对比算法具有更高的精度,更好的稳定性和通用性,证明了算法的有效性。
文摘In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both discretization techniques approximate correctly solution of advection equation and compare their accuracy and performance.
文摘Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the stability conditions for second order wave equation with central difference temporal discretization.The shape parameter of the radial basis functions not only has strong influence on the spatial stability and accuracy,but also has profound influence on the temporal stability.Numerical studies are conducted and show reasonable agreement with stability analysis.Conclusions of selecting shape parameters as well as spatial discretization for solution stability are also presented.
