After all the structural parameters are identified, the unknown earthquake-induced ground motion is finally constructed by solving a first-order differentiation equation.
The solution is found by solving a first order system of differential equations in the unknown amplitudes of the displacements and stresses.
Other studies [15, 17] have proposed a prediction filter-based binaural noise PSD estimator where the diffuse noise PSD was obtained by solving a second-order equation formulated using a channel prediction model.
The commonly used parabolic trough and cylindrical reflectors do not provide a uniform concentration on the receiving tube; therefore, in this paper a reflector profile design that uniformly concentrate the sunlight onto the receiver was attempted and was accomplished by solving a second order differential equation numerically.
We approach surface design by solving a linear third order Partial Differential Equation (PDE).
Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential.
After proper linearization of the equations of motion, boundary conditions, and contact conditions, the natural frequencies and mode shapes of the elastica can be obtained by solving a system of eighteen first-order differential equations with shooting method.
The framework consists of two steps: first, from a dense initial knot vector, a set of active knots is selected at which certain order derivative of the spline is discontinuous by solving a sparse optimization problem; second, we further remove redundant knots and adjust the positions of active knots to obtain the final knot vector.
The model is based on the Jansen-Rit model and the dynamics of the average PSP in each neuronal population x m is obtained by solving a system of 14 second-order differential equations: (7) d 2 x m t d t 2 = − 2 k m b m d x m t d t − k m 2 x m t + G m k m p m + ∑ n = 1 14 Γ n m S x n t, where n = 1,…, 14, and m = 1,…, 14.
The acoustic velocity perturbation, apart from one amplitude and one phase term, is common to the two cases, and is calculated in a second way, by solving a modified form of Mathieu's equation, with imaginary and hyperbolic, hence non-periodic, coefficients.
