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The error caused by choosing a finite number of rectangles as opposed to an infinite number of them is a truncation error in the mathematical process of integration. In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals An expression of general interest is the local truncation error of a method
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That is, it is the quantity if refers to the exact value and to the numerical approximation. 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 Causes of truncation with computers, truncation can occur when a decimal number is typecast as an integer
The second, usually called truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.
In general, a method with lte (local truncation error) is said to be of k th order
