Sentence examples for with the aid of computation from inspiring English sources

With the aid of computation we have that M 1 = π π 4 20 32 + 5 π = 1.

With the aid of symbolic computation, the unknown expansion coefficients associated with this choice of basis functions are shown to permit analytic resolution.

In addition, with the aid of parallel computation, large scale fracture closure and contact problems can be successfully simulated using our proposed dynamic fracture closure model (DFCM) with very modest computation times.

In this paper, the exp-function method, with the aid of symbolic computation systems, in particular Maple, has been applied to the Richards equation to evaluate its effectiveness and reliability, and to reach a more generalized solution of the problem.

As a result, a series of explicit solutions expressed in the Jacobi elliptic functions for them are successfully found with the aid of symbolic computation program.

With the aid of symbolic computation program, a series of exact solutions expressed in the Jacobi elliptic functions for the two equations are successfully found.

With the aid of symbolic computation Maple, solutions (30), (32) and (33) have been verified by substituting them into Eq. (1).

Of course, the softWith cannotheell whaidthe user wants, but it can help the user tofdo whomologyants as soon as he tells it.

In addition, the scheme can be also applied to investigate the tracking problem in the discrete-time systems and to generate automatically the scalar controller in computer with the aid of symbolic-numeric computation.

The computations are performed with the aid of the computer algebra systems Maple and Maxima.

The correlations were studied with the aid of a neural computation.