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Such a system is exactly solved using the exponential matrix method which is calculated by means of an expansion with a very fast convergence ratio.
The model can be exactly solved, using an optimal control method known as Pontryagin's maximum principle [ 45, 46].
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The transport equation for the VOF is numerically solved using exactly the same method for the flow solver.
This is exactly the single-source-shortest-path problem and it can be solved using Dijkstra's algorithm [ 38].
A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly.
Both contracts are exactly solved.
Kitaev, A. Anyons in an exactly solved model and beyond.
The corresponding time-dependent Schrödinger equation can be exactly solved.
Given Equation 1 for [ T C ], the above differential equation can be exactly solved analytically.
Of course, nobody should be economically exploited in order to meet the demand but banning foreigners from using surrogacy services doesn't exactly solve the problem.
However, most fractional differential equations are very difficult to exactly solve, so numerical and approximation techniques have to be used.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com