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For theoretical convergent accuracy (O tau^{q} + h^{p})), the convergent order about step length h can be approximated by mbox{Rate} = log_{2}frac{operatorname{Err} tau,h)}{operatorname{Err}(2^{ - p / q}tau,h / 2)}.
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Good convergent trend and accuracy are observed.
It is shown that the new integrators are convergent and the accuracy of the new integrators is improved as ∥M∥ grows large.
Especially, it is super-convergent about time accuracy.
The results show that the methods are convergent with a good accuracy.
Several examples are analyzed to validate the accuracy and convergent efficiency of the proposed beam element, and the results are compared with theoretical and numerical solutions.
Letting (alpha=0.3) and (p=1.52), the numerical results at (t=1) in time with (M=300) are displayed in Table 2, while the corresponding results in space with (N=5mbox000) are tabulated in Table 3, where our method yields the convergent approximationswith the desirable accuracy.
The SIAS has demonstrated good internal consistency, test-retest reliability, convergent validity and diagnostic accuracy [ 13, 28, 29].
In addition, the proposed method has superior accuracy to the convergent method described in the IMO guidelines.
This scheme is conditionally stable, convergent, and provides second-order accuracy with respect to time and space.
For smooth flow geometries, such as the plane Poiseuille flow which is studied here, the method combines the advantages of a high accuracy, exponentially fast convergent with mesh refinement and spectral approximation with those of an efficient numerical implementation well suited for a vector/parallel computer architecture.
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CEO of Professional Science Editing for Scientists @ prosciediting.com