Sentence examples for step by step integration from inspiring English sources

The optimization procedure is performed by sequential Simplex algorithm, while Newmark's beta method for step by step integration is used to find the dynamic response of the structure.

The final coupled equation of motion of entire system has been solved by a step by step integration, and for minimum tip deflection of the barrel, a GA has been then used in order to optimize the some parameters of the absorber.

By using the variation-of-constant formula and the step-by-step integration method, integrating the second equation of system (4) from 0 to t for (0< t leq tau), we obtain I t)=e^{- mu_{1}+gamma)t} biggl(phi_{2}(0)+int^{t}_{0}F bigl(S(xi)phi _{2}(xi-tau)e^{(mu_{1}+gamma)xi}, dxibigr) biggr).

Explicit expressions are then obtained through a step-by-step integration scheme, with five integral constants determinable from the boundary conditions at the cylindrical surface in the Saint Venant's sense.

The implicit Newmark step-by-step integration method is used to directly integrate the equation of motion, and then it is solved for the incremental displacement using the Newton Raphson iteration method, in which the stiffness matrix is updated at each increment to consider the geometrical and material nonlinearities and to speed the convergence rate.

Dynamic analysis is based on step-by-step integration schemes.

The responses are compared with step-by-step integration solutions.

Step-by-step integration is also used to solve the nonlinear single machine model.

The ASF model can be modelled with DAEs and solved with step-by-step integration.

Moreover, a step-by-step integration scheme able to solve the sensitivity equations is also studied.

The solution for the dynamic problem adopts implicit step-by-step integration (Newmark-beta) method (Bathe 1982; Chopra 1995).