Question

If the order of a discretized equation is ‘k’, what does it mean?

(a) The last term of the equation is of (k+1)^th power

(b) The last term of the equation is of k^th power

(c) Truncation error is proportional to (k-1)^th power

(d) Truncation error is proportional to k^th power

I have been asked this question in exam.

Origin of the question is Discretization Aspects in chapter Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

The correct option is (d) Truncation error is proportional to k^th power

The best I can explain: When a discretized equation is said to be of the order ‘k’, it means that the last term has (k-1)^th power and the first term of the truncated equation has k^th power. For example, in spatial derivative, the first term of the truncated equation will be proportional to (∆x)^k.