Sentence examples for by the implicit midpoint from inspiring English sources

In addition, we provide several examples to demonstrate that the conserved quantities of the equation are well preserved by the implicit midpoint time integrator.

We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-point sixth-order compact scheme.

Recall also that the implicit midpoint rule (IMR) [13] generates a sequence by the recursion process (2.3).

For the ordinary differential equation x'=f(t), qquad x 0)=x_{0}, (1.1) the implicit midpoint rule generates a sequence ({x_{n}}) by the recursion procedure x_{n+1}=x_{n}+hf biggl(frac{x_{n}+x_{n+1}}{2} biggr),quad nge0, (1.2) where (h>0) is a stepsize.

The implicit midpoint rule (IMR) for nonexpansive mappings is established.

The implicit midpoint rule (IMR) for nonexpansive mappings in a Hilbert spaceH, inspired by the IMR for ordinary differential equations [6 12], was introduced in [13].

The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces is established.

(1.4) The idea is to use contractions to regularize the implicit midpoint rule for nonexpansive mappings.

The idea was to use contractions to regularize the implicit midpoint rule for nonexpansive mappings.

In the present paper we will apply the viscosity technique to the implicit midpoint rule for nonexpansive mappings.

The implicit midpoint rule is one of the powerful numerical methods for solving ordinary differential equations and differential algebraic equations.