Taylor's series for transcendental functions have an infinite number of terms, but when approximating these functions with a finite number of terms, a truncation error is created. This error is defined as the difference between the true (analytical) derivative of a function and its derivative obtained by numerical approximation. For example, glycerin fractionation for PSA production has an estimated truncation error much larger than Cap-xylene production. The “truncation error T (x, h)” associated with the “predictor stage” of the “Milne—Hamming” method is given by.
The step size is normally estimated according to the truncation error in the current iteration, and a tolerance is used to control the size of the truncation error. The global truncation error is the sum of all local truncation errors in all iterations, assuming a perfect knowledge of the true solution in the initial time step. Having estimated the truncation error of the integration in the next iteration, a decision can be made as to whether to accept or reject the step size. Obtain a global truncation error limit for the second-order Adams-Moulton algorithm applied to a problem, assuming that the corrector is satisfied exactly after each step.
In Table 1, the truncation error estimated from upstream loss varies depending on the choices of hybridization methods and different technologies. In this method of error handling, the primary local truncation error remains less than a prescribed tolerance, so that the allowed error is under control. The “truncation error T (x, h)” associated with the “corrective stage” of the “Milne—Hamming” method is given by. The term truncation originates from the fact that numerical methods can be compared with a truncated Taylor series.
