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The benefits of using continuation are clearly demonstrated for both codes for a large class of problems.
New iterative methods for the solution of the unsymmetrical dual variable system are developed and are proven to converge for a large class of problems.
When applied to computing the adjoint associated with Burgers' equation, the Monte Carlo approach is faster for a large class of problems while preserving sufficient accuracy.
An intermediate algorithm, initially built to allow a clearer analysis by introducing separate time steps for external field and self-field integration, turned out to be useful by its own, for a large class of problems.
It has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features.
It can be concluded that this method is a very powerful and efficient technique to find the exact solutions for a large class of problems.
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This technique is particularly useful for solving a large class of problems involving discrete-continuous PBEs such as polymerization-depolymerization, aerosol dynamics, etc.
You can actually prove that not for any possible problem, but there is a large class of problems for which relaxing the problem this way allow you to get the exact solution.
Actually, the result was extended to more general operators, such as Δ p, under some suitable restrictions in order to solve a large class of problems (see for example the problems considered recently in the work of Covei [44]).
The method is quite general and may be applied to a large class of problems.
Such kind of switching controlled systems model a large class of problems in applied science.
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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