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The accuracy of the analytical sensitivity analysis is verified by finite difference computations.
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For consistency with previous finite difference computations (Caracas and Cohen 2005), we calculated the full elastic tensor to confirm that we obtained the same elastic velocities within error.
The proposed numerical scheme is then tested on the standard micromagnetic problem no. 4. In the numerical computations, the spatial discretization is obtained by finite difference technique and the magnetostatic field is computed through the Fast Fourier Transform method.
They discretized time domain by finite difference method.
The Jacobian is probably best evaluated by finite difference methods.
The equation (8a) can be represented by finite difference.
They solved this example by finite difference and finite element methods.
Furthermore, we can choose between modules that involve approximate computation of the needed derivatives by finite differences, and modules that expect the derivatives of the objective function to be provided by the routine that calls them.
Equations were discretised by finite differences.
The problem is discretized by Finite Differences.
In practice though, we replace derivatives by finite differences.
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