Sentence examples for by using the iteration from inspiring English sources

By using the iteration technique and comparison arguments, we have established sufficient conditions for the global stability of the coexistence equilibrium and the predator-extinction equilibrium.

The solution to the energy equation by using the iteration method needs the factor of relaxation of 0.5 and, the number of iteration is about 3400.

By using the iteration process (1.9) and Panyanak's fixed point result (Theorem 1.9), they proved Δ-convergence and strong convergence theorems for total asymptotically nonexpansive mappings on (operatorname{CAT}(0)) spaces.

Also, it is an open problem whether it is possible to prove the convergence theorem of a finite family of continuous mappings on an arbitrary interval by using the iteration methods in this paper.

It is well known that various assumptions in the previous literature have been made on the reaction term (f x,t,u,K*u)) (we have (K*u=0), t, or ((x,t))) such as monotonicity, positivity, convexity, concavity, or boundedness, etc., but these assumptions can be relaxed considerably (if not altogether) by using the iteration scheme (cf. [10, 24, 26]).

Boundedness of eigenfunctions is obtained by using the Moser iteration.

The results on existence and attractivity are obtained by using the Picard iteration method and Schauder's fixed point theorem.

For static deformations of a plate, the pull-in parameters are found by using the displacement iteration pull-in extraction method.

In an attempt to remove this gap, they gave a partial answer to the question raised by Panyanak by using the following iteration scheme.

Next, a 3D model of transformer for electromagnetic-thermal coupling is designed, and the heat sources of joints and temperature distribution are calculated by using the equivalent iteration of the JBF.

In 1922, Banach's contraction mapping principle appeared [1] and it was known for its simple and elegant proof by using the Picard iteration.