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As for the time advancing, starting from an explicit method, a linearized implicit scheme is generated, in which the flux Jacobian is computed through automatic differentiation.
In the MDR method, a linearized model of a perturbed CNT is first transformed into modal coordinates derived from the pristine system, taking into account the differences in the numbers of degrees of freedom for the pristine CNT and the CNT with MVDs.
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Then, a second-order TVD scheme is applied for the Burgers equation, and a linearized implicit finite difference method is used for the BBM equation.
A simple method of linearizing such a source is discussed.
To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems.
The perturbation analysis method of linearizing a transient mathematical system and solving the resultant eigenvalue differential equations for stability is automated using a numerical algorithm.
Since it is a difficult task to solve the planning model, a specific method for linearizing short circuit currents will be proposed in Section 4.
Finally, when the distance from the MU to more than two APs is estimated and assuming known the positions of these APs, an MUltilateration method that linearizes the problem of finding the MU position is implemented.
However, each model that has been reduced using our method can be linearized and checked for local observability and controllability.
The other methods considered are linearized and comparisons are made for a relaxation problem and a radiation diffusion problem.
In the first method we linearize the equilibrium equations written making null the gradient of the free energy of the system with respect to the corresponding ξr whilst in the second one we make successive unidimensional searches solving the equations for ξr.
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