Sentence examples for by numerical methods that from inspiring English sources
What remains is a partial differential equation that can be solved either explicitly or by numerical methods that can be employed to price zero coupon bonds and interest rate derivatives of any maturity.
Solutions to these models are either by linear approximations of the non-linear source, by other approximations of such non-linearity, or by numerical methods that frequently are heavily dependent of the mesh size for a successful convergence.
These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh resolution down to the finest scales and multiscale methods capable of capturing the large scale components of the solution on macroscopic meshes are needed.
These equations are solved by a numerical method that can be implemented on a spreadsheet to predict the position of the valve disk as a function of time for given valve characteristics, operating conditions, and installation parameters.
The contribution of the present paper is in introducing a numerical method to improve the automatic characterization of thin films by increasing the effectiveness of numerical methods that take into account the macroscopic shape of the tip.
These pdes are solved by employing an explicit finite-difference numerical method that yields the infiltration, the infiltration rate, the depth to the wetting front, the rate of runoff, and the depth of runoff everywhere on the slope during external wetting.
While these scales of fracture should be analyzed by numerical methods, macrofracture that occurs after the crack "emerged" from the representative unit cell where it originated can be considered using available analytical techniques.
This is solved by numerical methods demonstrating that the ky component is coupled to only stabilizing quantities while the kx component couples to the competing stabilizing and destabilizing parameters.
Comparison of the Pcmax presented in this paper with the empirical results from the curve or surface calculated by numerical method indicates that the relative error of Pcmax is less than 0.0039%.
