Sentence examples for by the numerical methods from inspiring English sources

The analytical methods have nearly been replaced by the numerical methods due to their higher accuracy and accessibility of computation facilities.

Remark The constant λ in Equations (2.2) and (2.7) can be solved directly by constant initial value and constant boundary values (or by the numerical methods).

The exact expression of P u * is not easily obtained and can be found by the numerical methods, such as the bisection method.

Solution of the Schrodinger equation including the above potentials has been done by the numerical methods in the above-mentioned works.

However, it is well known that the accuracy of structural analysis is largely dependent on the idealization of the structures and that the errors involved in it are much greater than those caused by the numerical methods.

The optimal solution to the subproblem (P2-2) is achieved at ( widehat{beta}={beta}^ ), where β* is the point at which η d,EE reaches its maximum for β ∈ [0, + ∞) and is obtained by solving the equation ( frac{d{eta}_{d,mathrm{E}mathrm{E}}}{dbeta }=0 ), as shown in Appendix 4. The exact expression of β* is not easily obtained and can be found by the numerical methods, such as the bisection method.

Linear stability analysis is given by applying the numerical methods to the test equation.

The geodynamic processes of mineralization are simulated by the numerical method built on the FLAC3D platform.

The ship responses in moderate seas are very well calculated by the numerical method.

A mathematical model for the process was established, and solved by the numerical method.

The generated system of differential equations was solved by the numerical method of Runge Kutta Fehlberg using the software Maple 8®.