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Nonlinear problems require many additional order conditions to be satisfied in order for a method to have a certain order of accuracy.
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The order of these modules does not indicate a certain order of events in a patient.
Moreover, further extrapolations can raise the order of accuracy of the method indefinitely (although beyond a certain point the lower errors will be overtaken by Monte Carlo errors).
We present the order of accuracy of the schemes and in order to show its convergence we prove they are stable under certain conditions.
Digital voltmeters generally have a higher order of accuracy than analogue instruments.
It is proved here that the eigenvalues of certain matrices appearing in these nonlinear systems are always 0, regardless of the number of spatial dimensions of the PDEs, or the chosen order of accuracy of the ADER-WENO method.
for the fourth order of accuracy difference problem (2.4).
Hence, the second order of accuracy difference scheme is more accurate comparing with the first order of accuracy difference scheme.
Numerical results confirm the designed fourth order of accuracy.
The methods can be designed for arbitrary order of accuracy.
However, certain computational MHD problems would be much benefited if the schemes had third and higher orders of accuracy.
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