Sentence examples for implicit formula from inspiring English sources
The proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces.
Such systems can be efficiently treated by a class of implicit explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula.
The resulting algorithm preserves the stability of the employed implicit formula and thus it has strong stability properties, e.g. it is not affected by the Courant condition or by physical stiffness such as that associated with the critical conditions of interfacial deformation.
One is required to solve the dilation equation to obtain a wavelet basis in an implicit formula.
An implicit formula for the mode(s) of the T-R{GL} families of distributions is presented in the following theorem.
(See [1].) In the nonautonomous case with constant delays, it has been proved by Pituk [2] that the value of the limit can be characterized in an implicit formula by using a special solution of the adjoint equation to (1.4) and the initial values.
Various algebraic boundary formulas for vorticity are investigated including new implicit formulas of the third and fourth order.
The solution includes implicit formulae for saturation, polymer, and salt concentrations and front trajectories of the components.
To avoid this difficulty, we have developed an efficient, fully-implicit time-integration algorithm based on a mathematically rigorous combination of implicit formulas with a Jacobian-free three-dimensional Newton method.
We excluded the exponentiated Rayleigh and exponentiated Weibull distributions because the FIM of the exponentiated Rayleigh distribution contains highly non-linear implicit formulae (Kundu and Raqab 2005), and the FIM of exponentiated Weibull distribution is not completely known (Pal et al. 2006).
When using the implicit Euler formula and the shifted Grünwald formula, it has been shown that the related discretizations lead to a linear system whose coefficient matrix has a Toeplitz-like structure.
