What is the Formula for Truncation Error?

Truncation error is defined as the difference between true (analytical) derivative and its derivative obtained by numerical approximation. Learn more about its formula and sources here.

What is the Formula for Truncation Error?

The error Rn is commonly referred to as the truncation error of the finite difference formula. This type of error is the difference between the true (analytical) derivative of a function and its derivative obtained by numerical approximation. It originates from the fact that numerical methods can be compared with a truncated Taylor series. To understand the relationship between local and global truncation errors, an additional concept called zero stability is needed.

It is clear that, regardless of the value of r, which is always greater than zero, the main term of the truncation error represents a fourth-order dissipative process that complements the physical dissipation of the diffusion equation. 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. Therefore, including a tolerance as a constraint on the size of the truncation error is ineffective, since each ODE would require a different value, and it is difficult to define the minimum step size uniquely because of the problem of different units. In Table 1, the truncation error estimated from upstream loss varies depending on the choices of hybridization methods and different technologies.

For each iteration, the step size is normally estimated according to the truncation error in that iteration. Given an infinite series, if only the first three terms are used, then one can find the truncation error of x% 3d0,75.The allowed truncation error, known as tolerance, is typically used to control the accuracy of integration. Truncation errors in Life Cycle Assessment (LCA) result from cutting off missing flows during boundary selection. Occasionally, by mistake, rounding errors (the consequence of using finite-precision floating-point numbers in computers) are also called truncation errors, especially if numbers are rounded by cutting.

In this method of error handling, primary local truncation errors remain less than a prescribed tolerance so that allowed errors are under control. Truncation errors are not the only source of errors in numerical resolution of initial value problems using difference formats; there is also a rounding error at each step of calculation.

Charlotte Wilson
Charlotte Wilson

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