Sentence examples for extending the solution from inspiring English sources

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

This approach takes into account the a priori structural constraints of the synthesis problem, analytically extending the solution to the subdomain of synthesis as well as finding the tolerances for small perturbations of the objective functional.

Extending the solution beyond wave breaking imposes significant challenge as can be illustrated in the case of multipeakons given by u ( t, x ) = ∑ i = 1 n p i ( t ) e − | x − q i ( t ) |, (5.1).

By extending the solution of a given ordinary differential equation (ODE) into the complex domain, one has the possibility, instead of asking for a global solution for an ODE, to look for solutions locally and obtain a more global result by analytic continuation.

The remaining part from the right hand side can be written in the form | x N + 1 | p R N + 1 ( 1 + Φ ( Δ z N + 1 z N + 1 ) ), where Δ z N + 1 is evaluated by extending the solution z from the interval [ 0, N − 1 ] to [ 0, N ].

Therefore, researchers have investigated extending the solution-processed layers [4 6].

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

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.

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

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