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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.
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
The condition number of a problem is the ratio of the relative change in the solution to the relative change in the input. [3] A problem is well-conditioned if small relative changes in input result in small relative changes in the solution.
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 ]
The Global Offset Table, or GOT, is a section of a computer program's (executables and shared libraries) memory used to enable computer program code compiled as an ELF file to run correctly, independent of the memory address where the program's code or data is loaded at runtime. [1]
[1] [2] The term truncation comes from the fact that these simplifications often involve the truncation of an infinite series expansion so as to make the computation possible and practical. Examples [ edit ]
In databases and computer networking data truncation occurs when data or a data stream (such as a file) is stored in a location too short to hold its entire length. [1] Data truncation may occur automatically, such as when a long string is written to a smaller buffer , or deliberately, when only a portion of the data is wanted.
This page was last edited on 28 February 2012, at 15:06 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.