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First, the coupled hygrothermal field along the radius of a rotating circular disk is achieved by solving the coupled hygrothermal equations, and then the dynamic equilibrium is solved by utilizing the finite difference method.
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The dynamic equations of equilibrium are solved by a combination of Navier's approach and a Laplace transform technique.
The equilibrium problem is solved by the DSG3 finite element method.
The lower level problem is the user equilibrium assignment model, which is solved by the Gradient projection algorithm.
The toll design problem is formulated as a mixed-integer mathematical programming with equilibrium constraints (MPEC) model, which is solved by a Hybrid GA (Genetic Algorithm)–CA method.
The problem is solved by perturbation method to find equilibrium configurations of DNA at different modes that can be excited.
The game is solved by backward induction and we characterize the equilibrium outcomes of this game.
The mass balance equations describing linear reaction chromatography with multiple components under equilibrium and non-equilibrium conditions are solved by means of the Laplace transformation.
The equilibrium equations are solved by a preconditioned conjugate gradient algorithm and the optimization part is solved using sequential convex programming.
The nonlinear post-buckling equilibrium equations are solved by Crisfield Ramm arc-length method in conjunction with the modified Newton Raphson technique.
Both the network equilibrium and design models are solved by effective solution algorithms and demonstrated with numerical examples.
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