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To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.
With the consistency condition (22), the Hamiltonian (21) becomes a single site model which can be solved exactly using a P-function based method introduced by Drummond and Walls [15].
The mDSM cannot be solved exactly using CPLEX in a reasonable amount of run time.
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The proposed MOMILP model is solved exactly using an augmented ε-constrained method.
In this approach, the interior unit cell problem is solved exactly using the elasticity approach.
Each subplate buckling problem is solved exactly using the Levy approach and the two solutions brought together by matching the continuity equations at the separated interface.
Each sub-plate buckling problem is solved exactly using the Levy approach and the two solutions brought together by the continuity equations at the separated interface.
The dynamic problem is solved exactly using a recurrence relationship up to any accuracy desired, by deriving the dynamic stiffness matrix for circular and annular membrane elements.
In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved exactly using the present parameter estimate and one sample of this input is applied to the system.
In contrast, with [ET] in activated lymphocytes estimated to be 0.04 μM based on TK1 tetramers of 100 kDa and an enzyme concentration of 4 μg/ml [ 4], in some cells [ET] could reach 0.1 μM, and at this concentration, and much more so if [ET] reached 0.6 μM, drastic differences in the shape of the response are obtained if Eq. (2) is solved exactly using ODEs [ 12].
This scenario can be solved exactly by using techniques similar to those presented here.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com