Hi, can anyone explain to me what do we mean by START-UP ERRORS in numerical solution (methods). any ref. around in this area...

Many thanks

You have to provide some initial condition for your problem. The difference between this initial guess and the final solution is the "start-up error" you refer to.

For example, one may initialize the flowfield around a body with freestream conditions. This doesn't represent the final flowfield, and as the solution converges, this error is reduced.

Generally, the closer the initialization is to the actual solution, the smaller the start-up error, and the faster the problem will converge.