Sentence examples for extend the solution from inspiring English sources

In order to extend the solution to a maximal interval we can apply the Theorem 2.3 [[14], p. 97].

In some cases, it is desirable to extend the solution to the interval [ 0, N ], see Remark 2.1 hereafter.

Thus, z ( x ) can be used to extend the solution y ˆ ( x ) on [ 0 ; a 2 ].

It is possible to extend the solution on the right of to some where the solution will assume the value.

Now we need to extend the solution ϕ of equation (3.1) to the domain ((-infty,xi^)) and ((xi^,+infty)).

This procedure can be repeated to extend the solution to the entire interval [0, T] in finitely many steps.

To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis.

Now we need estimates which allow us to extend the solutions to the whole interval ([0, T]) and pass to limit as (mrightarrowinfty) and (epsilonrightarrow0). Hence, uniform estimates with respect to m and ϵ are needed.

Finally, extending the solution uniquely to the closed interval [ 0, 1 ], we reach the result.

Gurakan et al. [22] extended the solution of [21] to adapt more network structures: relay channel and multiple access channel.

Note that despite the fact that the case n = 2 is solved in the previous section, the new material presented below extends the solution to all the cases.