Question

Advantages of numerical method over analytical method

Answer 1

First of all, it should be emphasised that the "numerical approach" is not automatically equivalent to the "approach with use of computer", although we usually use numerical approach to find the solution with use of computers. That is because of the high computer performance incomparable to abilities of human brain. Numerical approach enables solution of a complex problem with a great number (but) of very simple operations. It is perfect for the computer which is basically a very fast moron :-)

I think that we can distinguish two main situations when numerical methods are used instead of analytical methods:

1. When analytical solution of the mathematically defined problem is possible but it is time-consuming and the error of approximation we obtain with numerical solution is acceptable. In this case the calculations are mostly made with use of computer because otherwise its highly doubtful if any time is saved. It is also individually to decide what do we mean by "time-consuming analytical solution". In my discipline even very simple mechanical problems are solved numerically simply because of laziness...

2. When analytical solution is impossible, this means that we have to apply numerical methods in order to find the solution. This does not define that we must do calculations with computer although it usually happens so because of the number of required operations.

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