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In use of the Galerkin and complex normal form methods, the approximate analytical solution of the nonlinear equation is obtained, which has been corroborated by the numerical simulation.
We first discuss two reduced-order methods, the approximate inertial manifold and the proper orthogonal decomposition, and show that these methods can be used to obtain a reduced-order system that can accurately describe the dynamics of the KSE.
Of the three phase-correction methods, the approximate linear phase-correction method was the most tolerant of axis decenter from the optical axis, providing acceptable diffraction-limited correction performance.
For both HDG methods, the approximate vector field converges with the optimal order of k + 1 in the L2-norm, when polynomials of degree k are used to represent all the approximate variables.
In this paper, we consider, based on the projection methods, the approximate solvability for a system of generalized relaxed cocoercive nonlinear variational inequalities in Hilbert spaces.
MSE obtained using the BOMP algorithm is compared to pilot symbol-based Moose [1], Classen [2] methods, the approximate MLE [9], and the p-algorithm [5] for CFO value ε=0.03.
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Some of these techniques are moment space method, characteristic function method, moments method, and the approximate Fourier series method.
Based on the Lindstedt-Poincaré method, the approximate solution of the dispersion relation is derived.
In this method, the approximate fatigue damage of mooring line will be calculated from Weibull equation.
Using the modified version of He's homotopy perturbation method the approximate analytic solution is obtained.
Then, using dimensionless and perturbative method, the approximate analytical solution for simplified heat transfer equation has been obtained.
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