What about Numerical approximation errors  

Many often we do numerical approximations, and we must take care of several problem who comes within, we use numerical approximation when finding an analytical solution to a differential equation is not always a practical option, numerical approximations lead to solutions that are much more readily available.

Nevertheless the are some issues related to this process, the trick to constructing a viable numerical solution of a differential is identifying a reliable approximation of the derivative.

Errors acquired during the construction of a numerical solution come from two sources: roundoff and truncation, roundoff error arises from the limited precision of computer arithmetic. The problem is compounded in that the binary representation of many fractions is irrational, enhancing the effects of the roundoff error.

The second source of error is called truncation error, this error arises when we make discrete approximations of continuous functions. This error can be, to a certain extent, limited by making the step-sizes in the discrete function as small as possible.

Now we now in what we go to be careful when we do numerical approximations, and there are few ways to minimize this errors and we will see them later on this blog.