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where λ0 = τ/2h2, ψ M = 0 and F j ( 1 ) = V dip ( x j ) * | ψ j ( 1 ) | 2. The above method is implicit, unconditionally stable.
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Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure.
Q oS-based methods are implicit and non-intrusive which makes them an appealing choice.
The proposed methods are implicit, unconditionally stable and of second order in space and time directions.
Mention that the results yielded by most of the existing consensus network building methods are implicit and generally not easy to interpret.
And so the equation (1.1) admits the trivial solution x ( t ) ≡ 0. Since the numerical method (1.5) is implicit, the question of existence and uniqueness arises.
Moreover, in [5], Song and Chen introduced two iterative methods (one is implicit and the other is explicit) and established the strong convergence of such two methods in certain Banach spaces, if T satisfies the weakly inward condition and Fix ( T ) ≠ ∅.
The second method is an implicit finite difference method and unconditionally stable.
Furthermore, the method is partially implicit in order to increase stability of the computation.
One method is the implicit condensation method where the effects of membrane displacements are condensed into the nonlinear stiffness terms of the bending equations.
The basis of the present method is an implicit Ito Taylor expansion of the displacement and velocity vectors followed by a replacement of the multiple stochastic integrals by a set of random variables with simplified, discrete probability distributions.
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