Hence, the modified Adomian decomposition method (MADM) is utilized to obtain an analytical solution for bucking and pull-in instability of the actuator.
The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula.
A simple fracture mechanics problem with an analytical solution was also utilized for validation of the XFEM code.
At least one study has recently been published utilizing a MC method in the forward mode in lieu of an analytical solution [ 13].
Due to difficulties in finding an analytical solution, the assumed modes method is utilized to obtain an approximate solution to the problem.
The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method.
It was evaluated by an analytical solution.
The accuracy of the semi-analytical model is confirmed by comparing the results with the numerical simulation (CMG, 2015) and an analytical solution (Kappa, 2015).
As an analytical solution does not exist in such a complex geometry, different numerical solutions are compared.
But we can do an analytical solution to illustrate this point.
