Sentence examples for apply continuation from inspiring English sources

The idea is to define a simplified starting problem and then to apply continuation techniques.

The optimality criteria is used as optimizer and to avoid local minima we apply continuation of an exponent that controls the stiffness associated with intermediate design variables.

By applying continuation and observing the multipliers during the continuation, we easily obtain an estimate of the 14-dimensional robustness region.

In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws.

In this section, we shall apply the continuation theorem of Mawhin's coincidence degree theory to establish the global existence of at least one positive periodic solution.

To apply the continuation theorem, we investigate the operator equation begin{aligned} &x^{Delta}(t)=lambda biggl[a(t -b(t -bp bigl(x(t) bigr)-frac {c(t)exp (y(t))}{alpha(t)+bigl(t) ex t(x(t))+m(t)exp (y(t))} bigr -frac^{Delta}(t)=lambigr -frac-d(t)+frac{c(t)exp (x(t))}{alpha(t)+beta(t) exp (x(t))+m(t)exp (y(t))}{alpha].

Numerically, we use q 1 ( 0 ) = q 2 ( 1 ) = δ, δ ≪ 1 for the search, and apply a continuation-collocation strategy to keep track of grid points and function evaluations used.

By applying Mawhin continuation theorem, some new existence results are established.

After applying numerical continuation techniques and ideas from dynamical systems theory, complete bifurcation diagrams are constructed.

By applying the continuation theorems, Gaines and Mawhin proved that the Rayleigh equation can support periodic solutions.

By applying the continuation theorem and some analytic techniques, we shall establish several new criteria for the existence of positive periodic solutions for the considered problem.