Sentence examples for by an implicit method from inspiring English sources

The slurry mass balance equation is an elliptic PDE and is solved by an implicit method, and the shock-capturing methods discussed earlier are not applied to solve this PDE.

Thus the present Monte Carlo procedure has to be supplemented by an implicit method for properly advancing discrete perpendicular velocity increments in time.

Then, by virtue of the existence and uniqueness theorem, we introduced an implicit method and analyzed its strong convergence.

The stiff source terms are solved by an implicit trapezoidal method of integration.

The equations of motion are obtained using the principle of virtual work and are solved in the time domain by an implicit Newmark method.

We apply the same asymptotic analysis to a discrete version of the problem, in which the frequency variable is discretized by the multigroup method, the direction variable by the discrete-ordinates method, the time variable by the fully implicit method, and the spatial variable by a subcell-balance method.

Theorem 3.1 Suppose that F ( T ) ∩ ( A + B ) − 1 0. Then the net { x t } defined by the implicit method (3.1) converges strongly, as t → 0, to a point x ˜ ∈ F ( T ) ∩ ( A + B ) − 1 0, which is the unique solution of the variational inequality (3.2).

Proposition 3.1 The net { x t } generated by the implicit method (3.2) is bounded.

Every injection rate of each segment of wellbore is solved by linear implicit method to enhance the stability of numerical equations.

Then, as α m → 0, the sequence {x m } generated by the implicit method (3.1) converges to x ̃ ∈ F i x ( T ).

Theorem 3.3 The net { x t } generated by the implicit method (3.2) converges in norm, as t → 0 +, to the unique solution x ∗ of the following variational inequality: x ∗ ∈ Γ, 〈 ( I − f ) x ∗, x − x ∗ 〉 ≥ 0, x ∈ Γ. (3.13).