truncation error उदाहरण वाक्य

For linear multistep methods, an additional concept called zero-stability is needed to explain the relation between local and global truncation errors.
Truncation errors are committed when an iterative method is terminated or a mathematical procedure is approximated, and the approximate solution differs from the exact solution.
A slightly different formulation for the local truncation error can be obtained by using the Lagrange form for the remainder term in Taylor's theorem.
Thus, for extremely small values of the step size, the truncation error will be small but the effect of rounding error may be big.
A finite difference scheme is compact in the sense that the discretised formula comprises at most nine point truncation error terms in the finite difference equation.

In explicit filtering, an LES filter is applied to the discretized Navier Stokes equations, providing a well-defined filter shape and reducing the truncation error.
If the solution y has a bounded second derivative and f is Lipschitz continuous in its second argument, then the global truncation error ( GTE ) is bounded by
The global truncation error is the error at a fixed time t, after however many steps the methods needs to take to reach that time from the initial time.
Often, truncation error also includes discretization error, which is the error that arises from taking a finite number of steps in a computation to approximate an infinite process.
Occasionally, round-off error ( the consequence of using finite precision floating point numbers on computers ) is also called truncation error, especially if the number is rounded by truncation.