The Jacobian matrix obtained after linearizing the system at the equilibrium point P is given as Eq. (4). $$J_{P} = \left[ {\begin{array}{*{20}c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ { - a} & { - 1} & { - c} \\ \end{array} } \right]$$ (4) ...
descent search direction in the case the of positive definite Jacobian.The convergence analysis of the proposed method was discussed under suitable conditions.Preliminary results presented show that the proposed method is efficient andIn addition, the method can find wider application in real-life ...
It should be noted that \(\underline{D}\,F({Y}_{j})\) is the m × m Jacobian matrix of F at Yj. The Lyapunov exponent is obtained by calculating the eigenvalues of the matrix (\(\underline{D}\,{F}^{K})^{\prime} \underline{D}\,{F}^{K}\) where \(\underline{D}\...
Then, the calculations were repeated for the model with 16 Jacobian points, which did not affect the obtained results. It should be noted that the Jacobian points are points used to check the Jacobian ratio which is a measure of mesh quality. Change from 4 to 16 points does not affect ...
A more efficient alternative is to pose the interface residual problem as a non-linear Newton–Raphson (N–R) iterative procedure, leading to the so called Jacobian-based resolution schemes. However, the use of a black-box coupling scheme intentionally precludes the exact calculation of the interf...
It should be noted that F is well defined and has continuous partial derivatives on an open set of ℝ𝑛Rn, J(x) represents the Jacobian matrix [44]. It was assumed that solution 𝐱̲x¯ can be written as 𝐱̲=x¯= x0 + s, where x0 is some known guess of x, and...
Some new exact solutions of jacobian elliptic function about the generalized Boussinesq equation and Boussinesq Burgers equation. Chin. Phys. B 2008, 17, 403. [Google Scholar] [CrossRef] Mehdinejadiani, B.; Jafari, H.; Baleanu, D. Derivation of a fractional Boussinesq equation for modelling ...
iOS: The native refresh rate of the display is controlled by the AppleProMotionfeature. When ProMotion is disabled in the project (default for new projects), the native refresh rate is 60 Hz. When ProMotion is enabled, the native refresh rate is 120 Hz on the iOS displays that support ...
If the jth parameter is known, we can add the known information to the Jacobian matrix. The elements of the jth column of the J matrix are all 0. Therefore, the J matrix can be rewritten as below: J=⎡⎢⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢...
The input decoupling transformation is formally determined as the right inverse of the transpose of the full-vehicle Jacobian matrix. This approach overcomes the problem of a system such as a ground vehicle system that has reduced control effectiveness. The overall active control scheme is similar ...