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The first and second derivative methods were also employed to analyze and compare the variation of these hydrochar properties.
The general, algebraic framework allows for the calculation of gradients using both the Direct and Adjoint derivative methods.
The influence of various physicochemical parameters of the model was also analyzed based on sensitivity studies using experimental design and derivative methods based on the DASPK 3.0 code.
Here we evaluate the approach using image gradient operators, and we present comparative qualitative and quantitative results for both first and second order derivative methods.
However, the maximum decrease rates and the variation regions of hydrochar properties (determined by the first and the second derivative methods) show similar profiles for different feedstock.
The first modification involves the introduction of collocation at the two end points of the integration interval in addition to the Gaussian interior collocation points and the second involves the introduction of a different class of basic second derivative methods.
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Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method.
The shape gradient function and the optimality conditions for this problem are derived theoretically using the material derivative method and the adjoint variable method.
We derive the shape gradient function by using the material derivative method and apply it to the free-form optimization method for determining the optimal shape.
The 3 point derivative method is faster than Hamming-window parabolic filtration method, so we conclude that the 3 point derivative method is optimal for 3D FBP.
We aim to introduce the Fourier-spectral derivative method into the Poincare maps method.
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