On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function.
These include multi-derivative methods proposed by Twizell and Tirmizi [15], collocation algorithms based on interpolating and approximating subdivision schemes by Ma and Silva [3], sinc collocation method by Nurmuhammad et al. [16], homotopy perturbation technique for a special fourth order BVP by Momani and Noor [17] and finite difference method by Usmani [18], and Chen and Li [19].
The recently developed multi-group derivative of TINTE called MGT (multi-group TINTE) is able to handle up to 43 neutron energy groups.
They calculate a multi-scale derivative at center of every local interest point to encode motion information.
In summary (Table 1), by using different transgenic UAS-hUCP3 insertions and their multi-insertion derivative (UAS-hUCP3-high), we generated transgenic lines expressing hUCP3 ubiquitously at half (A and B), equal (C and D) or higher (G and H) levels than endogenous levels in mouse skeletal muscle.
[11] studied the linear system with multi-order Caputo derivative and derived a sufficient condition on Lyapunov global asymptotical stability.
In all cases, the use of multi-point spatial derivative approximations are explored to find an optimum.
Although, the function F ( z ) is in general multi-valued, its derivative F ′ is a single-valued analytic function on G.
More recently, applications have included classes of nonlinear equations with multi-order fractional derivative, and this motivates us to develop a numerical scheme for their solutions.
Different to the general time fractional diffusion equation, the constitutive equation not only has a multi-term time derivative but also possesses a special time fractional operator on the spatial derivative, which is challenging to approximate.
Meanwhile in order to further improve computational efficiency and overcome the difficulty that the level set method cannot generate new material interfaces during the optimization process, the multi-material topological derivative analysis is incorporated into the level set method for topological optimization.
