Sentence examples for construction of solutions from inspiring English sources

Descartes's goal in La Géométrie was to achieve the construction of solutions to geometric problems by means of instruments that were acceptable generalizations of ruler and compass.

The application of the theory is illustrated by the construction of solutions for a four-step PSA process.

A technique for the numerical construction of solutions for an essentially non-linear hybrid-type system of constituent equations is proposed.

Using commutation methods (i.e., N = 1 supersymmetry) underlying Miura's transformation, an explicit construction of solutions of the modified Korteweg-de Vries equation, given a solution of the (ordinary) Korteweg-de Vries equation, is provided.

It is used to provide a probabilistic approach to the regularity of harmonic maps, thus completing the probabilistic construction of solutions to the small-image harmonic map Dirichlet problems described in Kendall (Proc. London Math. Soc. (3) 61990990), 371-406).

Section 3 is devoted to the construction of solutions and the proof of our result.

As illustrated using a literature example, it also facilitates computation and construction of solution diagrams.

The method we apply is based on the iterative construction of solution estimates and repetitive application of the Grönwall inequality.

Another approach to numerical computation of Lyapunov quantities which uses the passage to the polar coordinates and the procedure of sequential construction of solution approximations is related with the obtaining of approximations of system solution, see [2], they also could be seen in [6, 7].

Determining the group invariant solutions, construction of new solutions for the system from the known ones, classification of the group invariant solutions, reduction of the order of ordinary differential equations, detection of linearizing transformations, and mapping solutions to other solutions are the other important applications of Lie groups in the theory of differential equations.

The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition.