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Numerical methods which solve the ODE fall into several categories [7, 8, 9, 10, 11] which depend on the case study.
The mathematical programming (MP) methods which solve the continuous sub-problems provide only one local optimum which depends strongly on the initialization.
In this paper, we present the development of new explicit group relaxation methods which solve the two dimensional second order hyperbolic telegraph equation subject to specific initial and Dirichlet boundary conditions.
We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions.
This classification fundamentally differentiates between "projecting methods", where controllability is monitored during the process design to predict the trade-offs between design and control, and the "integrated-optimization methods" which solve the process design and the control-systems design at once within an optimization framework.
A significant performance improvement by GAHP/GABHP methods using d=3 over LSMnC/LSMnS methods (which solve the hypergraph partitioning problem for d=2) may imply that d should be increased to 4 or more for better performance.
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The other is the spectral bin method, which solves growth equations by discretizing the PSD with tens of bins covering these modes (Khain et al. [2000], [2008]).
To calculate added resistance, three different numerical approaches are applied: the strip method, the Rankine panel method, and the Cartesian grid method, which solves the Euler equation.
In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich's extragradient method, which solves variational inequality problems.
Because the dual problem is differentiable, it can be solved by the classic sub-gradient method, which solves the optimal problem based on the gradient and the suitable step size [28].
The genetic algorithm (GA) is a stochastic method which solves problems considering a large number of generations, while the deterministic methods such as sequential quadratic programming (SQP), which are sensitive to the initial points, can solve problems faster.
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