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The relation between local and global truncation errors is slightly different from in the simpler setting of one-step methods. For linear multistep methods, an additional concept called zero-stability is needed to explain the relation between local and global truncation errors.
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Download QR code; Print/export Download as PDF; Printable version; In other projects ... Example A: Find the truncation in calculating the first derivative of () ...
called the local Artin symbol, the local reciprocity map or the norm residue symbol. [4] [5] Let L⁄K be a Galois extension of global fields and C L stand for the idèle class group of L. The maps θ v for different places v of K can be assembled into a single global symbol map by multiplying the local
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In general, a method with (+) LTE (local truncation error) is said to be of kth order. The region of absolute stability for the backward Euler method is the complement in the complex plane of the disk with radius 1 centered at 1, depicted in the figure. [ 4 ]
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Another example, encoding an alphabet of size 10 (between 0 and 9) requires 4 bits, but there are 2 4 − 10 = 6 unused codes, so input values less than 6 have the first bit discarded, while input values greater than or equal to 6 are offset by 6 to the end of the binary space. (Unused patterns are not shown in this table.)