The function ) (E) is analytic in e and converges uniformly in E for any fixed positive e since the norm decays exponentially with n. The desired i /( ) can then be obtained as the limit [Pg.285]

Whence it follows immediately that the explicit scheme converges uniformly [Pg.320]

Whence it follows immediately that the explicit scheme converges uniformly with the rate 0(r + h2). [Pg.320]

It is clear that the Jacobian qg = 1 — of this transformation converges uniformly to the unit on as J —> 0. Introduce the notations [Pg.103]

We give a brief survey afforded by the above results scheme (II) converges uniformly with the same rate as in the grid L2(w )-norm (see (35)) if and only if condition (39) holds. The stability condition (39) in the space C for the explicit scheme with cr = 0, namely r < coincides with the [Pg.316]

We note in passing that is determined by formula (47), due to which scheme (49) converges uniformly with the rate 0(r - - /i ) under the aforementioned conditions on sequences of special grids. [Pg.480]

Theorem 2 If u x) C G), that is, a solution possesses continuous derivatives in (5 = 0 + F of the first four orders, then the difference scheme converges uniformly with the rate O(h ), that is, it is of second-order accuracy, so that estimate (16) is valid. [Pg.271]

Under such a choice of the computational algorithm the accuracy of scheme (49) will be given special investigation. We are going to show that it converges uniformly with the rate 0 h + r " ) in the case of smooth functions k x) and [Pg.476]

A solution of this problem can be estimated in a similar way as was done in the preceding section, but with = r i ai. In concluding this section we establish through such an analysis that scheme (59)-(61) converges uniformly at the rate 0 h ) [Pg.198]

More a detailed proof of convergence of this scheme is concerned with the form (74) and a priori estimates obtained in Chapter 6, Section 2 and so it is omitted here. As a final result we deduce that scheme (70) converges uniformly with the rate 0(Tm,r + h2). [Pg.486]

As approximation schemes, wavelets trivially satisfy the Assumptions 1 and 2 of our framework. Both the L2 and the error of approximation is decreased as we move to higher index spaces. More specifically, recent work (Kon and Raphael, 1993) has proved that the wavelet transform converges uniformly according to the formula [Pg.170]

Having no opportunity to touch upon this topic, we refer the readers to the aforementioned chapters of the manograph The Theory oof Difference Schemes , in which the method of extraction of stationary nonhomogeneities was employed with further reference to a priori estimates of z. The forward difference scheme with cr = 1 converges uniformly with the rate 0 h + r) due to the maximum principle. [Pg.495]

We conclude that any solution w t, s) coincides with the unique periodic solution of (3.67), as soon as so t) > s, independently of the initial condition. This is a very strong stability statement of finite time convergence, uniformly on bounded subsets s. For further details see [34]. [Pg.100]

See also in sourсe #XX -- [ Pg.165 ]

See also in sourсe #XX -- [ Pg.122 ]

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